Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50%	0.4%	49.6%	10
50.2%	0.2%	49.6%	11
50.2%	0.1%	49.7%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.1s (38.2%)

Results

1.1s	8256×	body	256	valid
1.0ms	14×	body	256	invalid

preprocess89.0ms (3.1%)

Algorithm

2×	egg-herbie

Rules

658×	`div-sub_binary64`
631×	`fma-def_binary64`
417×	`times-frac_binary64`
408×	`associate-/l*_binary64`
382×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	19	9
2	50	9
3	111	7
4	236	7
5	531	7
6	1618	7
7	5638	7
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Outputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify57.0ms (2%)

Algorithm

1×	egg-herbie

Rules

658×	`div-sub_binary64`
631×	`fma-def_binary64`
417×	`times-frac_binary64`
408×	`associate-/l*_binary64`
382×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	19	9
2	50	9
3	111	7
4	236	7
5	531	7
6	1618	7
7	5638	7

Stop Event

1×	node limit

Counts

1 → 4

Calls

Call 1

Inputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Outputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

eval1.0ms (0%)

Compiler: Compiled 25 to 15 computations (40% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	1	5

Error

0.1b

Counts

5 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))
✓	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(exp.f64 (+.f64 (*.f64 x x) -1))
0.0ms	x	@	inf	(exp.f64 (+.f64 (*.f64 x x) -1))
0.0ms	x	@	-inf	(exp.f64 (+.f64 (*.f64 x x) -1))

rewrite51.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

611×	`pow1_binary64`
569×	`add-log-exp_binary64`
569×	`log1p-expm1-u_binary64`
569×	`expm1-log1p-u_binary64`
557×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	126	7
2	1571	7

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(exp.f64 (+.f64 (*.f64 x x) -1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))))

simplify67.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

596×	`times-frac_binary64`
482×	`fma-def_binary64`
304×	`associate-l_binary64`
286×	`fma-neg_binary64`
284×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	316
1	156	312
2	458	300
3	2464	293
4	6229	293

Stop Event

1×	node limit

Counts

34 → 40

Calls

Call 1

Inputs
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 1)
(pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)
(pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)
(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(pow.f64 (exp.f64 1) (fma.f64 x x -1))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))

Outputs
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(.f64 (+.f64 (.f64 x x) 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))
(fma.f64 (exp.f64 -1) (.f64 x x) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (exp.f64 -1)))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (.f64 1/2 (pow.f64 x 4))))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)))))
(fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 (exp.f64 -1) (.f64 x x) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (exp.f64 -1))))
(fma.f64 (exp.f64 -1) (.f64 1/6 (pow.f64 x 6)) (.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (*.f64 1/2 (pow.f64 x 4)))))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (fma.f64 1/2 (pow.f64 x 4) (.f64 1/6 (pow.f64 x 6)))))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(exp.f64 (fma.f64 x x -1))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(exp.f64 (fma.f64 x x -1))
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 1)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 1) (fma.f64 x x -1))
(pow.f64 (E.f64) (fma.f64 x x -1))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(exp.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(exp.f64 (fma.f64 x x -1))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))

eval12.0ms (0.4%)

Compiler: Compiled 440 to 334 computations (24.1% saved)

prune53.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Error

0.0b

Counts

41 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))
▶	0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
▶	0.7b	(exp.f64 -1)
▶	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 x) x)
	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.0b	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 18 to 9 computations (50% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(pow.f64 (exp.f64 x) x)
1.0ms	x	@	inf	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
0.0ms	x	@	-inf	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
0.0ms	x	@	0	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
0.0ms	x	@	inf	(pow.f64 (exp.f64 x) x)

rewrite49.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`pow1_binary64`
528×	`add-log-exp_binary64`
528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
514×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	130	15
2	1468	15

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

Inputs
(pow.f64 (exp.f64 x) x)
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 x) (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x x))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (+.f64 -1 (.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 -1 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (+.f64 -1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 -1 (*.f64 x x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 x) (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x x))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 -1 (*.f64 x x)))))))

simplify55.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
467×	`associate-l_binary64`
405×	`associate-r_binary64`
316×	`distribute-rgt-in_binary64`
311×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	455
1	199	405
2	619	387
3	3254	382
4	6495	382

Stop Event

1×	node limit

Counts

50 → 58

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(-.f64 (+.f64 1 (pow.f64 (exp.f64 x) x)) 1)
(*.f64 (pow.f64 (exp.f64 x) x) 1)
(*.f64 1 (pow.f64 (exp.f64 x) x))
(*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (pow.f64 1 x) (pow.f64 (exp.f64 x) x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
(log.f64 (exp.f64 (pow.f64 (exp.f64 x) x)))
(cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))
(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))
(log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) x)))
(exp.f64 (*.f64 x x))
(-.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)
(pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)
(pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))
(log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 -1 (*.f64 x x)))

Outputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (fma.f64 x x (*.f64 1/2 (pow.f64 x 4))))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x (*.f64 1/2 (pow.f64 x 4)))))
(fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1)))
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(*.f64 (fma.f64 x x 1) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (*.f64 (pow.f64 x 4) (exp.f64 -1))))
(+.f64 (.f64 (fma.f64 x x 1) (exp.f64 -1)) (.f64 1/2 (*.f64 (pow.f64 x 4) (exp.f64 -1))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (.f64 (pow.f64 x 4) (exp.f64 -1)))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (.f64 (fma.f64 x x 1) (exp.f64 -1)) (.f64 1/2 (.f64 (pow.f64 x 4) (exp.f64 -1)))))
(fma.f64 (fma.f64 x x 1) (exp.f64 -1) (.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (.f64 1/6 (pow.f64 x 6)))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(-.f64 (+.f64 1 (pow.f64 (exp.f64 x) x)) 1)
(pow.f64 (exp.f64 x) x)
(*.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(*.f64 1 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2))
(pow.f64 (exp.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x)))
(pow.f64 (exp.f64 x) x)
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
(pow.f64 (exp.f64 x) x)
(*.f64 (pow.f64 1 x) (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) (+.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
(pow.f64 (exp.f64 x) x)
(log.f64 (exp.f64 (pow.f64 (exp.f64 x) x)))
(pow.f64 (exp.f64 x) x)
(cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))
(pow.f64 (exp.f64 x) x)
(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))
(pow.f64 (exp.f64 x) x)
(log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) x)))
(pow.f64 (exp.f64 x) x)
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(-.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

localize3.0ms (0.1%)

Compiler: Compiled 4 to 4 computations (0% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
	0.0b	(exp.f64 (+.f64 x 1))
✓	0.0b	(exp.f64 (+.f64 x 1))
✓	0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))

Compiler

Compiled 22 to 16 computations (27.3% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
0.0ms	x	@	-inf	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
0.0ms	x	@	inf	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
0.0ms	x	@	0	(exp.f64 (+.f64 x 1))
0.0ms	x	@	-inf	(exp.f64 (+.f64 x 1))

rewrite66.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`pow1_binary64`
795×	`add-log-exp_binary64`
793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
777×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	171	13
2	2224	13

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(exp.f64 (+.f64 x 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (+.f64 x 1)) x) (/.f64 1 (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (exp.f64 (+.f64 x 1))) (pow.f64 (exp.f64 (+.f64 x 1)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (+.f64 x -1)) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)) (exp.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (+.f64 x -1)) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)) (pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 x x -1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 x) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (E.f64) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (cbrt.f64 (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (sqrt.f64 (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (+.f64 x 1))))))))

simplify56.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

417×	`associate-/l*_binary64`
325×	`associate-/r*_binary64`
288×	`fma-def_binary64`
287×	`associate-*l/_binary64`
246×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	670
1	303	546
2	1000	531
3	3367	524

Stop Event

1×	node limit

Counts

63 → 78

Calls

Call 1

Inputs
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(exp.f64 1)
(+.f64 (*.f64 x (exp.f64 1)) (exp.f64 1))
(+.f64 (.f64 x (exp.f64 1)) (+.f64 (.f64 1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (exp.f64 1)))
(+.f64 (.f64 x (exp.f64 1)) (+.f64 (.f64 1/2 (.f64 (exp.f64 1) (pow.f64 x 2))) (+.f64 (.f64 1/6 (*.f64 (exp.f64 1) (pow.f64 x 3))) (exp.f64 1))))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 1 x))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(*.f64 (pow.f64 (exp.f64 (+.f64 x 1)) x) (/.f64 1 (exp.f64 (+.f64 x 1))))
(*.f64 (/.f64 1 (exp.f64 (+.f64 x 1))) (pow.f64 (exp.f64 (+.f64 x 1)) x))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(*.f64 (pow.f64 1 (+.f64 x -1)) (exp.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)) (exp.f64 (+.f64 x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (+.f64 x -1)) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)) (pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(+.f64 1 (expm1.f64 (+.f64 x 1)))
(-.f64 (+.f64 1 (exp.f64 (+.f64 x 1))) 1)
(*.f64 1 (exp.f64 (+.f64 x 1)))
(*.f64 (exp.f64 (+.f64 x 1)) 1)
(*.f64 (exp.f64 x) (E.f64))
(*.f64 (E.f64) (exp.f64 x))
(*.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (cbrt.f64 (exp.f64 (+.f64 x 1))))
(*.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (sqrt.f64 (exp.f64 (+.f64 x 1))))
(pow.f64 (exp.f64 (+.f64 x 1)) 1)
(pow.f64 (E.f64) (+.f64 x 1))
(pow.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 3) 1/3)
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 3)
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) 2)
(pow.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (cbrt.f64 (+.f64 x 1)))
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 2))
(log.f64 (exp.f64 (exp.f64 (+.f64 x 1))))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 x 1))))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 x 1))))

Outputs
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(.f64 (+.f64 (.f64 x x) 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(/.f64 (fma.f64 x x 1) (E.f64))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))
(fma.f64 (exp.f64 -1) (.f64 x x) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (exp.f64 -1)))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (.f64 1/2 (pow.f64 x 4))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)))))
(fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 (exp.f64 -1) (.f64 x x) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (exp.f64 -1))))
(fma.f64 (exp.f64 -1) (.f64 1/6 (pow.f64 x 6)) (.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (*.f64 1/2 (pow.f64 x 4)))))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (+.f64 (.f64 1/2 (pow.f64 x 4)) (*.f64 1/6 (pow.f64 x 6)))))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (+.f64 1 x) (-.f64 x 1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (.f64 -1 (.f64 (-.f64 1 (.f64 -1 x)) (+.f64 1 (.f64 -1 x)))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 1)
(E.f64)
(+.f64 (*.f64 x (exp.f64 1)) (exp.f64 1))
(fma.f64 x (E.f64) (E.f64))
(+.f64 (.f64 x (exp.f64 1)) (+.f64 (.f64 1/2 (*.f64 (exp.f64 1) (pow.f64 x 2))) (exp.f64 1)))
(fma.f64 x (E.f64) (fma.f64 1/2 (.f64 (.f64 x x) (E.f64)) (E.f64)))
(fma.f64 x (E.f64) (fma.f64 (.f64 1/2 (E.f64)) (.f64 x x) (E.f64)))
(.f64 (E.f64) (+.f64 (+.f64 x 1) (.f64 (*.f64 x x) 1/2)))
(+.f64 (.f64 x (exp.f64 1)) (+.f64 (.f64 1/2 (.f64 (exp.f64 1) (pow.f64 x 2))) (+.f64 (.f64 1/6 (*.f64 (exp.f64 1) (pow.f64 x 3))) (exp.f64 1))))
(fma.f64 x (E.f64) (fma.f64 1/2 (.f64 (.f64 x x) (E.f64)) (fma.f64 1/6 (*.f64 (E.f64) (pow.f64 x 3)) (E.f64))))
(fma.f64 x (E.f64) (fma.f64 1/2 (.f64 x (.f64 x (E.f64))) (fma.f64 1/6 (*.f64 (E.f64) (pow.f64 x 3)) (E.f64))))
(+.f64 (fma.f64 x (E.f64) (E.f64)) (.f64 (E.f64) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 1/6 (pow.f64 x 3)))))
(.f64 (E.f64) (+.f64 (+.f64 x 1) (+.f64 (.f64 (.f64 x x) 1/2) (.f64 1/6 (pow.f64 x 3)))))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 x 1))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 x 1))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 x 1))
(exp.f64 (+.f64 1 x))
(exp.f64 (+.f64 x 1))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (+.f64 x 1))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (+.f64 x 1))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (+.f64 x 1))
(exp.f64 (-.f64 1 (*.f64 -1 x)))
(exp.f64 (+.f64 x 1))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (exp.f64 (+.f64 x 1)) x) (/.f64 1 (exp.f64 (+.f64 x 1))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (/.f64 1 (exp.f64 (+.f64 x 1))) (pow.f64 (exp.f64 (+.f64 x 1)) x))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 1 (+.f64 x -1)) (exp.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)) (exp.f64 (+.f64 x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (+.f64 x -1)) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (+.f64 -1 x)) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 -1 x)))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)) (pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 x -1)))
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (*.f64 2 (+.f64 -1 x)))
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (+.f64 -2 (*.f64 x 2)))
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (fma.f64 x 2 -2))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(+.f64 1 (expm1.f64 (+.f64 x 1)))
(exp.f64 (+.f64 x 1))
(-.f64 (+.f64 1 (exp.f64 (+.f64 x 1))) 1)
(exp.f64 (+.f64 x 1))
(*.f64 1 (exp.f64 (+.f64 x 1)))
(exp.f64 (+.f64 x 1))
(*.f64 (exp.f64 (+.f64 x 1)) 1)
(exp.f64 (+.f64 x 1))
(*.f64 (exp.f64 x) (E.f64))
(exp.f64 (+.f64 x 1))
(*.f64 (E.f64) (exp.f64 x))
(exp.f64 (+.f64 x 1))
(*.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2))
(exp.f64 (+.f64 x 1))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 2) (cbrt.f64 (exp.f64 (+.f64 x 1))))
(exp.f64 (+.f64 x 1))
(*.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) (sqrt.f64 (exp.f64 (+.f64 x 1))))
(exp.f64 (+.f64 x 1))
(pow.f64 (exp.f64 (+.f64 x 1)) 1)
(exp.f64 (+.f64 x 1))
(pow.f64 (E.f64) (+.f64 x 1))
(exp.f64 (+.f64 x 1))
(pow.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 3) 1/3)
(exp.f64 (+.f64 x 1))
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 x 1))) 3)
(exp.f64 (+.f64 x 1))
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 x 1))) 2)
(exp.f64 (+.f64 x 1))
(pow.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))
(pow.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))) (hypot.f64 1 (sqrt.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (cbrt.f64 (+.f64 x 1)))
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 2))
(exp.f64 (+.f64 x 1))
(log.f64 (exp.f64 (exp.f64 (+.f64 x 1))))
(exp.f64 (+.f64 x 1))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 x 1)) 3))
(exp.f64 (+.f64 x 1))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 x 1))))
(exp.f64 (+.f64 x 1))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 x 1))))
(exp.f64 (+.f64 x 1))

eval76.0ms (2.6%)

Compiler: Compiled 1672 to 1217 computations (27.2% saved)

prune19.0ms (0.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	134	6	140

Error

0.0b

Counts

140 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))
✓	0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
✓	0.7b	(exp.f64 -1)
▶	0.3b	(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
▶	0.0b	(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))

Compiler

Compiled 53 to 37 computations (30.2% saved)

localize15.0ms (0.5%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 x) x)
	0.0b	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
	0.0b	(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))
✓	0.0b	(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))
✓	0.0b	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
	0.0b	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 41 to 11 computations (73.2% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
0.0ms	x	@	0	(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))
0.0ms	x	@	-inf	(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))

rewrite93.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`pow1_binary64`
618×	`add-log-exp_binary64`
618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
599×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	171	15
2	1752	15

Stop Event

1×	node limit

Counts

2 → 33

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) (*.f64 (/.f64 x 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) (+.f64 (/.f64 x 2) (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) (*.f64 2 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (*.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) (+.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) 2) (/.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (exp.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x x))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3) (pow.f64 (exp.f64 -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (*.f64 x x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 -1 (*.f64 x x)))))))

simplify70.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

571×	`unswap-sqr_binary64`
429×	`fma-def_binary64`
390×	`associate-/l/_binary64`
319×	`sqr-pow_binary64`
264×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	506
1	242	452
2	803	434
3	2888	429
4	5672	429

Stop Event

1×	node limit

Counts

57 → 68

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(-.f64 (+.f64 1 (exp.f64 (*.f64 x x))) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 x) (*.f64 (/.f64 x 2) 2))
(pow.f64 (exp.f64 x) (+.f64 (/.f64 x 2) (/.f64 x 2)))
(pow.f64 (exp.f64 x) (*.f64 2 (/.f64 x 2)))
(pow.f64 (sqrt.f64 (exp.f64 (*.f64 x x))) 2)
(pow.f64 (exp.f64 (*.f64 x x)) 1)
(pow.f64 (pow.f64 (exp.f64 x) (+.f64 x x)) 1/2)
(pow.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3) 1/3)
(pow.f64 (pow.f64 (exp.f64 x) 2) (/.f64 x 2))
(pow.f64 (cbrt.f64 (exp.f64 (*.f64 x x))) 3)
(pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(pow.f64 (pow.f64 (exp.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
(fabs.f64 (exp.f64 (*.f64 x x)))
(log.f64 (exp.f64 (exp.f64 (*.f64 x x))))
(cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (*.f64 x x))))
(log1p.f64 (expm1.f64 (exp.f64 (*.f64 x x))))
(exp.f64 (*.f64 x x))
(-.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)
(pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)
(pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))
(log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))
(cbrt.f64 (.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) (pow.f64 (exp.f64 -1) 3)))
(cbrt.f64 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (.f64 x x)) 3)))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 -1 (*.f64 x x)))

Outputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (fma.f64 x x (*.f64 1/2 (pow.f64 x 4))))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x (*.f64 1/2 (pow.f64 x 4)))))
(fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1)))
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(pow.f64 (exp.f64 x) x)
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(*.f64 (fma.f64 x x 1) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 (*.f64 1/2 (exp.f64 -1)) (pow.f64 x 4)))
(+.f64 (.f64 (fma.f64 x x 1) (exp.f64 -1)) (.f64 1/2 (*.f64 (pow.f64 x 4) (exp.f64 -1))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(*.f64 (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)) (exp.f64 -1))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 (.f64 1/2 (exp.f64 -1)) (pow.f64 x 4))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (.f64 (fma.f64 x x 1) (exp.f64 -1)) (.f64 1/2 (.f64 (pow.f64 x 4) (exp.f64 -1)))))
(fma.f64 (fma.f64 x x 1) (exp.f64 -1) (.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (.f64 1/6 (pow.f64 x 6)))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1))))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(-.f64 (+.f64 1 (exp.f64 (*.f64 x x))) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 x) (*.f64 (/.f64 x 2) 2))
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 x) (+.f64 (/.f64 x 2) (/.f64 x 2)))
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 x) (*.f64 2 (/.f64 x 2)))
(pow.f64 (exp.f64 x) x)
(pow.f64 (sqrt.f64 (exp.f64 (*.f64 x x))) 2)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 x x)) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (pow.f64 (exp.f64 x) (+.f64 x x)) 1/2)
(pow.f64 (exp.f64 x) x)
(pow.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3) 1/3)
(pow.f64 (exp.f64 x) x)
(pow.f64 (pow.f64 (exp.f64 x) 2) (/.f64 x 2))
(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))
(pow.f64 (pow.f64 (exp.f64 x) 2) (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (exp.f64 (*.f64 x x))) 3)
(pow.f64 (exp.f64 x) x)
(pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(pow.f64 (pow.f64 (exp.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
(pow.f64 (exp.f64 x) x)
(fabs.f64 (exp.f64 (*.f64 x x)))
(pow.f64 (exp.f64 x) x)
(log.f64 (exp.f64 (exp.f64 (*.f64 x x))))
(pow.f64 (exp.f64 x) x)
(cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3))
(pow.f64 (exp.f64 x) x)
(expm1.f64 (log1p.f64 (exp.f64 (*.f64 x x))))
(pow.f64 (exp.f64 x) x)
(log1p.f64 (expm1.f64 (exp.f64 (*.f64 x x))))
(pow.f64 (exp.f64 x) x)
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(-.f64 (+.f64 1 (exp.f64 (+.f64 -1 (*.f64 x x)))) 1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3) 1/3)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 3)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))) 2)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 2))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (*.f64 x x))) 3))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) (pow.f64 (exp.f64 -1) 3)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (.f64 x x)) 3)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (*.f64 x x)))))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

localize26.0ms (0.9%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
	0.0b	(pow.f64 (exp.f64 x) (+.f64 x x))
	0.0b	(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))
✓	0.0b	(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))
✓	0.0b	(pow.f64 (exp.f64 x) (+.f64 x x))
✓	0.2b	(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))

Compiler

Compiled 33 to 11 computations (66.7% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
1.0ms	x	@	0	(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
0.0ms	x	@	inf	(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))
0.0ms	x	@	-inf	(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
0.0ms	x	@	-inf	(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))

rewrite163.0ms (5.6%)

Algorithm

3×	egg-rewrite-iter-limit
3×	egg-rewrite
1×	batch-egg-rewrite

Rules

309×	`pow1_binary64`
309×	`pow1_binary64`
306×	`add-sqr-sqrt_binary64`
306×	`add-sqr-sqrt_binary64`
296×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	180	33
2	2652	33
0	6	11
1	129	1
2	2035	1
3	6188	1
0	6	11
1	129	1
0	5	9
1	110	1
2	1807	1
3	5821	1
0	5	9
1	110	1
0	9	16
1	180	16
2	2653	16
0	9	16

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	node limit

Counts

3 → 8

Calls

Call 1

Inputs
(sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))
(pow.f64 (exp.f64 x) (+.f64 x x))
(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x . 1)))))

((#(struct:change #<rule egg-rr> (2) ((x . 1)))))

((#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))) (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))) (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))))))

simplify57.0ms (2%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
532×	`associate-+l+_binary64`
472×	`associate-*l/_binary64`
289×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	562
1	146	548
2	392	462
3	1203	407
4	3025	379

Stop Event

1×	node limit

Counts

44 → 60

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
1
(+.f64 (*.f64 2 (pow.f64 x 2)) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 2 (pow.f64 x 4))))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 4/3 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 4)))))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
1
1
(pow.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))) 1)
(log.f64 (exp.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))) (.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))) (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(expm1.f64 (log1p.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(log1p.f64 (expm1.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(exp.f64 (log.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))

Outputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4))))
(+.f64 (fma.f64 x x 1) (*.f64 1/2 (pow.f64 x 4)))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x (*.f64 1/2 (pow.f64 x 4)))))
(fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1)))
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
(sqrt.f64 (exp.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))
(fabs.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 x) x)
1
(+.f64 (*.f64 2 (pow.f64 x 2)) 1)
(fma.f64 2 (*.f64 x x) 1)
(fma.f64 x (+.f64 x x) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 2 (pow.f64 x 4))))
(+.f64 (fma.f64 2 (.f64 x x) 1) (.f64 2 (pow.f64 x 4)))
(fma.f64 2 (*.f64 x x) (fma.f64 2 (pow.f64 x 4) 1))
(fma.f64 x (+.f64 x x) (fma.f64 2 (pow.f64 x 4) 1))
(fma.f64 2 (fma.f64 x x (pow.f64 x 4)) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 4/3 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 4)))))
(+.f64 (fma.f64 2 (.f64 x x) 1) (fma.f64 4/3 (pow.f64 x 6) (.f64 2 (pow.f64 x 4))))
(+.f64 (fma.f64 2 (.f64 x x) 1) (fma.f64 (pow.f64 x 6) 4/3 (.f64 2 (pow.f64 x 4))))
(fma.f64 x (+.f64 x x) (fma.f64 2 (pow.f64 x 4) (fma.f64 (pow.f64 x 6) 4/3 1)))
(fma.f64 2 (fma.f64 x x (pow.f64 x 4)) (fma.f64 (pow.f64 x 6) 4/3 1))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (exp.f64 2) (*.f64 x x))
(pow.f64 (exp.f64 x) (+.f64 x x))
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(*.f64 (fma.f64 x x 1) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (*.f64 (pow.f64 x 4) (exp.f64 -1))))
(+.f64 (.f64 (fma.f64 x x 1) (exp.f64 -1)) (.f64 (pow.f64 x 4) (*.f64 1/2 (exp.f64 -1))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)))
(*.f64 (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1)) (exp.f64 -1))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (.f64 (pow.f64 x 4) (exp.f64 -1)))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (.f64 (fma.f64 x x 1) (exp.f64 -1)) (.f64 (pow.f64 x 4) (.f64 1/2 (exp.f64 -1)))))
(fma.f64 (fma.f64 x x 1) (exp.f64 -1) (.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (.f64 1/6 (pow.f64 x 6)))))
(*.f64 (exp.f64 -1) (fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1))))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(.f64 (sqrt.f64 (exp.f64 (.f64 2 (pow.f64 x 2)))) (exp.f64 -1))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
1
1
(pow.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))) 1)
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(log.f64 (exp.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x)))) (.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))) (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(expm1.f64 (log1p.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(log1p.f64 (expm1.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (log.f64 (*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 x x))) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fabs.f64 (pow.f64 (exp.f64 x) x)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (+.f64 (*.f64 x x) -1))

eval74.0ms (2.6%)

Compiler: Compiled 2778 to 1718 computations (38.2% saved)

prune27.0ms (0.9%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	190	6	196

Error

0.0b

Counts

196 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))
✓	0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
✓	0.7b	(exp.f64 -1)
▶	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.0b	(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))

Compiler

Compiled 54 to 38 computations (29.6% saved)

localize30.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))
	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
✓	0.0b	(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))

Compiler

Compiled 35 to 18 computations (48.6% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))
0.0ms	x	@	inf	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
0.0ms	x	@	inf	(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))
0.0ms	x	@	-inf	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
0.0ms	x	@	-inf	(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))

rewrite75.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

931×	`pow1_binary64`
869×	`add-log-exp_binary64`
865×	`log1p-expm1-u_binary64`
865×	`expm1-log1p-u_binary64`
103×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	208	21
2	2639	21

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

Inputs
(pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (/.f64 (*.f64 0 x) 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))) (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))) 2) (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))) (sqrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (*.f64 x 1/2)) (exp.f64 (/.f64 (*.f64 0 x) 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) (*.f64 x 1/2)) (pow.f64 (exp.f64 x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) 2) (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (/.f64 (*.f64 0 x) 0))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 3) (pow.f64 (exp.f64 -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))))

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

41×	`associate-r_binary64`
37×	`sqr-pow_binary64`
34×	`associate-l_binary64`
25×	`fma-def_binary64`
21×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	319
1	214	319
2	756	319

Stop Event

1×

unsound

Counts

54 → 49

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(-.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)))) 1)
(.f64 (exp.f64 (/.f64 (.f64 0 x) 0)) 1)
(.f64 1 (exp.f64 (/.f64 (.f64 0 x) 0)))
(.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 0 x) 0))) (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))) 2))
(.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 0 x) 0))) 2) (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
(.f64 (sqrt.f64 (exp.f64 (/.f64 (.f64 0 x) 0))) (sqrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
(.f64 (pow.f64 1 (.f64 x 1/2)) (exp.f64 (/.f64 (*.f64 0 x) 0)))
(.f64 (pow.f64 (exp.f64 x) (.f64 x 1/2)) (pow.f64 (exp.f64 x) (*.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) 2) (.f64 x 1/2)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 2))
(log.f64 (exp.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
(log.f64 (+.f64 1 (expm1.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)))))
(cbrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
(log1p.f64 (expm1.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
(exp.f64 (/.f64 (*.f64 0 x) 0))
(-.f64 (exp.f64 (log1p.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))))) 1)
(pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 1)
(pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 3) 1/3)
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))) 3)
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))) 2)
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 2))
(log.f64 (exp.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))
(log.f64 (+.f64 1 (expm1.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))))))
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 3))
(cbrt.f64 (.f64 (pow.f64 (exp.f64 (/.f64 (.f64 0 x) 0)) 3) (pow.f64 (exp.f64 -1) 3)))
(cbrt.f64 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (/.f64 (.f64 0 x) 0)) 3)))
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))
(exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))

Outputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/2 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 1/2 (pow.f64 x 4)))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 (*.f64 1/2 (exp.f64 -1)) (pow.f64 x 4)))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (pow.f64 x 6) (exp.f64 -1)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 (.f64 1/2 (exp.f64 -1)) (pow.f64 x 4))))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(*.f64 (exp.f64 (pow.f64 x 2)) (exp.f64 -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(-.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)))) 1)
1
(.f64 (exp.f64 (/.f64 (.f64 0 x) 0)) 1)
1
(.f64 1 (exp.f64 (/.f64 (.f64 0 x) 0)))
1
(.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 0 x) 0))) (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))) 2))
1
(.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 0 x) 0))) 2) (cbrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
1
(.f64 (sqrt.f64 (exp.f64 (/.f64 (.f64 0 x) 0))) (sqrt.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
1
(.f64 (pow.f64 1 (.f64 x 1/2)) (exp.f64 (/.f64 (*.f64 0 x) 0)))
1
(.f64 (pow.f64 (exp.f64 x) (.f64 x 1/2)) (pow.f64 (exp.f64 x) (*.f64 x 1/2)))
(pow.f64 (exp.f64 x) (.f64 2 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) 2) (.f64 x 1/2)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 2))
1
(log.f64 (exp.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
1
(log.f64 (+.f64 1 (expm1.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)))))
1
(cbrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 0 x) 0)) 3))
1
(expm1.f64 (log1p.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
1
(log1p.f64 (expm1.f64 (exp.f64 (/.f64 (*.f64 0 x) 0))))
1
(exp.f64 (/.f64 (*.f64 0 x) 0))
1
(-.f64 (exp.f64 (log1p.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))))) 1)
1
(pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 1)
1
(pow.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 3) 1/3)
1
(pow.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))) 3)
1
(pow.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))) 2)
1
(sqrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 2))
1
(log.f64 (exp.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))
1
(log.f64 (+.f64 1 (expm1.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))))))
1
(cbrt.f64 (pow.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0))) 3))
1
(cbrt.f64 (.f64 (pow.f64 (exp.f64 (/.f64 (.f64 0 x) 0)) 3) (pow.f64 (exp.f64 -1) 3)))
1
(cbrt.f64 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 (exp.f64 (/.f64 (.f64 0 x) 0)) 3)))
1
(expm1.f64 (log1p.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))
1
(log1p.f64 (expm1.f64 (exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))))
1
(exp.f64 (+.f64 -1 (/.f64 (*.f64 0 x) 0)))
1

eval15.0ms (0.5%)

Compiler: Compiled 615 to 528 computations (14.1% saved)

prune8.0ms (0.3%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	0	0
Picked	0	1	1
Done	1	4	5
Total	49	6	55

Error

0.0b

Counts

55 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(exp.f64 (+.f64 (*.f64 x x) -1))
✓	0.0b	(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
✓	0.7b	(exp.f64 -1)
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
	0.0b	(.f64 (exp.f64 -1) (.f64 (pow.f64 (exp.f64 x) (.f64 x 1/2)) (pow.f64 (exp.f64 x) (.f64 x 1/2))))

Compiler

Compiled 56 to 42 computations (25% saved)

regimes62.0ms (2.1%)

Counts

9 → 1

Calls

Call 1

Inputs
(exp.f64 -1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
(*.f64 (exp.f64 -1) (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))))
(.f64 (exp.f64 -1) (.f64 (pow.f64 (exp.f64 x) (.f64 x 1/2)) (pow.f64 (exp.f64 x) (.f64 x 1/2))))
(.f64 (exp.f64 -1) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))

Outputs
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))

Calls

9 calls:

35.0ms	(*.f64 x x)
9.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(-.f64 1 (*.f64 x x))
2.0ms	(neg.f64 (-.f64 1 (*.f64 x x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.0b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.0b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(*.f64 x x)`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 134 to 85 computations (36.6% saved)

regimes25.0ms (0.9%)

Counts

5 → 1

Calls

Call 1

Inputs
(exp.f64 -1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))

Outputs
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))

Calls

9 calls:

4.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
4.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(*.f64 x x)
2.0ms	(-.f64 1 (*.f64 x x))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.0b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.0b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(*.f64 x x)`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 83 to 57 computations (31.3% saved)

regimes24.0ms (0.8%)

Counts

4 → 1

Calls

Call 1

Inputs
(exp.f64 -1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))

Outputs
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))

Calls

9 calls:

4.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
4.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(*.f64 x x)
2.0ms	(neg.f64 (-.f64 1 (*.f64 x x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.0b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.0b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(*.f64 x x)`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 76 to 52 computations (31.6% saved)

regimes36.0ms (1.3%)

Accuracy

Total -0.6b remaining (-1152.4%)

Threshold costs -0.6b (-1152.4%)

Counts

3 → 1

Calls

Call 1

Inputs
(exp.f64 -1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Outputs
(exp.f64 (+.f64 (*.f64 x x) -1))

Calls

8 calls:

19.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
2.0ms	(-.f64 1 (*.f64 x x))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.1b	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
0.1b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.1b	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
0.1b	1	`(-.f64 1 (*.f64 x x))`
0.1b	1	`(-.f64 1 (*.f64 x x))`
0.1b	1	`(*.f64 x x)`

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	28	52

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 -1)

Outputs
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 (+.f64 x x)) (/.f64 x 2)))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 -1 x))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 -1)

Compiler

Compiled 39 to 30 computations (23.1% saved)

soundness224.0ms (7.7%)

Algorithm

2×	egg-herbie

Rules

658×	`div-sub_binary64`
631×	`fma-def_binary64`
571×	`unswap-sqr_binary64`
429×	`fma-def_binary64`
417×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	19	9
2	50	9
3	111	7
4	236	7
5	531	7
6	1618	7
7	5638	7
0	99	506
1	242	452
2	803	434
3	2888	429
4	5672	429

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 68 to 49 computations (27.9% saved)

end39.0ms (1.4%)

Compiler: Compiled 35 to 26 computations (25.7% saved)

Details

analyze3.0ms (0.1%)

sample1.1s (38.2%)

preprocess89.0ms (3.1%)

simplify57.0ms (2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite51.0ms (1.8%)

simplify67.0ms (2.3%)

eval12.0ms (0.4%)

prune53.0ms (1.8%)

localize10.0ms (0.3%)

series3.0ms (0.1%)

rewrite49.0ms (1.7%)

simplify55.0ms (1.9%)

localize3.0ms (0.1%)

localize13.0ms (0.5%)

series3.0ms (0.1%)

rewrite66.0ms (2.3%)

simplify56.0ms (1.9%)

eval76.0ms (2.6%)

prune19.0ms (0.6%)

localize15.0ms (0.5%)

series2.0ms (0.1%)

rewrite93.0ms (3.2%)

simplify70.0ms (2.4%)

localize26.0ms (0.9%)

series4.0ms (0.1%)

rewrite163.0ms (5.6%)

simplify57.0ms (2%)

eval74.0ms (2.6%)

prune27.0ms (0.9%)

localize30.0ms (1%)

series3.0ms (0.1%)

rewrite75.0ms (2.6%)

simplify16.0ms (0.6%)

eval15.0ms (0.5%)

prune8.0ms (0.3%)

regimes62.0ms (2.1%)

regimes25.0ms (0.9%)

regimes24.0ms (0.8%)

regimes36.0ms (1.3%)

simplify5.0ms (0.2%)

soundness224.0ms (7.7%)

end39.0ms (1.4%)

Profiling