Details

analyze5.0ms (0.4%)

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
50.2%	0%	49.8%	13
50.2%	0%	49.8%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample788.0ms (59.3%)

Results

774.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess29.0ms (2.2%)

Algorithm

2×	egg-herbie

Rules

417×	`times-frac_binary64`
412×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
350×	`associate-l_binary64`
200×	`distribute-rgt-in_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	1613	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 8 to 6 computations (25% saved)

simplify19.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

417×	`times-frac_binary64`
412×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
350×	`associate-l_binary64`
200×	`distribute-rgt-in_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	1613	7

Stop Event

1×	node limit

Counts

1 → 2

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))

prune2.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 25 to 17 computations (32% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series1.0ms (0.1%)

Counts

1 → 4

Calls

3 calls:

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

rewrite33.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

394×	`pow1_binary64`
361×	`add-log-exp_binary64`
361×	`log1p-expm1-u_binary64`
361×	`expm1-log1p-u_binary64`
353×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	90	7
2	971	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(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 (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 .f64 (exp.f64 (*.f64 x x)) (exp.f64 -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 1) (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 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 log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 (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 *.f64 (exp.f64 (*.f64 x x)) (exp.f64 -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 1) (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 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 log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))))))

simplify38.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

724×	`distribute-lft-out_binary64`
385×	`*-commutative_binary64`
380×	`fma-def_binary64`
341×	`distribute-rgt-out_binary64`
340×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	55	79
2	136	63
3	448	56
4	1828	56
5	3578	56
6	4583	56

Stop Event

1×	node limit

Counts

24 → 27

Calls

Call 1

Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))

Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (.f64 (exp.f64 -1) (.f64 x x)))
(.f64 (+.f64 (.f64 x x) 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (.f64 (exp.f64 -1) (*.f64 x x))))
(+.f64 (exp.f64 -1) (fma.f64 (exp.f64 -1) (.f64 x x) (.f64 (exp.f64 -1) (*.f64 (pow.f64 x 4) 1/2))))
(.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1)))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (.f64 (exp.f64 -1) (.f64 x x)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 (exp.f64 -1) (.f64 x x) (.f64 (exp.f64 -1) (.f64 (pow.f64 x 4) 1/2)))))
(fma.f64 (exp.f64 -1) (.f64 1/6 (pow.f64 x 6)) (.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1))))
(.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (pow.f64 x 6)) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (fma.f64 1/6 (pow.f64 x 6) (.f64 1/2 (pow.f64 x 4)))))

prune16.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Error

0.0b

Counts

28 → 2

Alt Table

Status	Error	Program
▶	0.0b	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
✓	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 300 to 229 computations (23.7% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 (fma.f64 x x -1))
✓	1.0b	(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
✓	1.5b	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))

series6.0ms (0.4%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
1.0ms	x	@	inf	(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
1.0ms	x	@	-inf	(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
0.0ms	x	@	inf	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))

rewrite39.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`pow1_binary64`
531×	`add-log-exp_binary64`
531×	`log1p-expm1-u_binary64`
531×	`expm1-log1p-u_binary64`
518×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	158	17
2	1481	17

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)

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 (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 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) 1/3))))) (#(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 .f64 (exp.f64 (.f64 x x)) (exp.f64 -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) 1/3) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3/2) 1/3) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3/2) 1/3))))) (#(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 (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 1) (fma.f64 x x -1))))) (#(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 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 log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))))) (#(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 exp.f64 (fma.f64 x x -1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (fma.f64 x x -1)) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3/2) (pow.f64 (exp.f64 (fma.f64 x x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) 3) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 3) (pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) 1) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (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 (.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (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 sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 x x -1) 3))))))

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (fma.f64 x x -1)) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3/2) (pow.f64 (exp.f64 (fma.f64 x x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) 3) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 3) (pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) 1) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (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 (*.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (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 sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 x x -1) 3))))))

simplify44.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

592×	`distribute-rgt-out_binary64`
333×	`*-commutative_binary64`
213×	`associate-l_binary64`
197×	`fma-def_binary64`
194×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	255
1	99	249
2	320	198
3	1322	190
4	2861	188
5	3353	188
6	4012	188

Stop Event

1×	node limit

Counts

59 → 58

Calls

Call 1

Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 -1) 3)
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (pow.f64 (exp.f64 -1) 3))
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 6))) (+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4))))))

Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (.f64 (exp.f64 -1) (.f64 x x)))
(.f64 (+.f64 (.f64 x x) 1) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (.f64 (exp.f64 -1) (*.f64 x x))))
(.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1)))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (.f64 1/2 (pow.f64 x 4))))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (.f64 (exp.f64 -1) (.f64 x x)))))
(fma.f64 (exp.f64 -1) (.f64 1/6 (pow.f64 x 6)) (.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1))))
(.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (pow.f64 x 6)) (+.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 1/6 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 4)))))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 -1) 3)
(exp.f64 -3)
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (pow.f64 (exp.f64 -1) 3))
(fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3))
(.f64 (+.f64 (.f64 (*.f64 x x) 3) 1) (exp.f64 -3))
(fma.f64 (exp.f64 -3) (.f64 x (.f64 x 3)) (exp.f64 -3))
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3)) (.f64 9/2 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3))))
(fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (fma.f64 9/2 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3)))
(+.f64 (exp.f64 -3) (.f64 (exp.f64 -3) (+.f64 (.f64 (.f64 x x) 3) (.f64 (pow.f64 x 4) 9/2))))
(.f64 (exp.f64 -3) (+.f64 (.f64 x (.f64 x 3)) (+.f64 1 (.f64 (pow.f64 x 4) 9/2))))
(.f64 (exp.f64 -3) (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 9/2) (.f64 x (.f64 x 3)))))
(+.f64 (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 6))) (+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4))))))
(fma.f64 9/2 (.f64 (pow.f64 x 6) (pow.f64 (exp.f64 -1) 3)) (+.f64 (fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3)) (.f64 9/2 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3)))))
(fma.f64 9/2 (.f64 (pow.f64 x 6) (pow.f64 (exp.f64 -1) 3)) (fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (fma.f64 9/2 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 x x) 3) 1) (exp.f64 -3)) (.f64 (*.f64 (exp.f64 -3) 9/2) (+.f64 (pow.f64 x 4) (pow.f64 x 6))))
(+.f64 (exp.f64 -3) (.f64 (exp.f64 -3) (+.f64 (.f64 x (.f64 x 3)) (.f64 9/2 (+.f64 (pow.f64 x 4) (pow.f64 x 6))))))
(.f64 (exp.f64 -3) (+.f64 (.f64 9/2 (+.f64 (pow.f64 x 4) (pow.f64 x 6))) (+.f64 1 (.f64 x (.f64 x 3)))))
(.f64 (exp.f64 -3) (+.f64 1 (+.f64 (.f64 x (.f64 x 3)) (.f64 9/2 (+.f64 (pow.f64 x 4) (pow.f64 x 6))))))

prune54.0ms (4.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	85	2	87

Error

0.0b

Counts

87 → 2

Alt Table

Status	Error	Program
▶	0.0b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))
✓	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 1136 to 903 computations (20.5% saved)

localize9.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3)
	1.0b	(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
	1.5b	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
✓	1.5b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))
0.0ms	x	@	0	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3)
0.0ms	x	@	inf	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))
0.0ms	x	@	inf	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3)
0.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))

rewrite37.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`pow1_binary64`
533×	`add-log-exp_binary64`
533×	`log1p-expm1-u_binary64`
533×	`expm1-log1p-u_binary64`
520×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	201	17
2	1525	17

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))
(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3)

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (fma.f64 x x -1)) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (exp.f64 (fma.f64 x x -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (*.f64 (fma.f64 x x -1) 3/2)) (exp.f64 (*.f64 (fma.f64 x x -1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) 3) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 3) (pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) 1) (exp.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (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 (*.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2) (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 sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 x x -1) 3))))))

simplify39.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

604×	`distribute-rgt-out_binary64`
353×	`*-commutative_binary64`
256×	`distribute-rgt-in_binary64`
231×	`exp-sum_binary64`
213×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	335
1	105	329
2	330	278
3	1364	270
4	3018	268
5	3976	268

Stop Event

1×	node limit

Counts

67 → 60

Calls

Call 1

Inputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 -1) 3)
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (pow.f64 (exp.f64 -1) 3))
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 6))) (+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4))))))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)

Outputs
(exp.f64 -1)
(+.f64 (exp.f64 -1) (*.f64 (exp.f64 -1) (pow.f64 x 2)))
(+.f64 (exp.f64 -1) (.f64 (exp.f64 -1) (.f64 x x)))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2))))
(+.f64 (exp.f64 -1) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (.f64 (exp.f64 -1) (*.f64 x x))))
(.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1)))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (.f64 1/2 (pow.f64 x 4))))
(+.f64 (exp.f64 -1) (+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4))) (*.f64 (exp.f64 -1) (pow.f64 x 2)))))
(+.f64 (exp.f64 -1) (fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (.f64 (exp.f64 -1) (.f64 x x)))))
(fma.f64 (exp.f64 -1) (.f64 1/6 (pow.f64 x 6)) (.f64 (exp.f64 -1) (+.f64 (*.f64 1/2 (pow.f64 x 4)) (fma.f64 x x 1))))
(.f64 (exp.f64 -1) (+.f64 (+.f64 (fma.f64 x x 1) (.f64 1/2 (pow.f64 x 4))) (*.f64 1/6 (pow.f64 x 6))))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (+.f64 (.f64 1/6 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 4)))))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 -1) 3)
(exp.f64 -3)
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (pow.f64 (exp.f64 -1) 3))
(fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3))
(fma.f64 (.f64 3 (pow.f64 (exp.f64 -1) 3)) (.f64 x x) (pow.f64 (exp.f64 -1) 3))
(fma.f64 (.f64 x x) (.f64 3 (exp.f64 -3)) (exp.f64 -3))
(.f64 (exp.f64 -3) (+.f64 1 (.f64 x (*.f64 x 3))))
(+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3)) (.f64 9/2 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3))))
(fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (fma.f64 9/2 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3)))
(+.f64 (exp.f64 -3) (.f64 (exp.f64 -3) (+.f64 (.f64 (pow.f64 x 4) 9/2) (.f64 x (.f64 x 3)))))
(.f64 (exp.f64 -3) (+.f64 (.f64 x (.f64 x 3)) (+.f64 1 (.f64 (pow.f64 x 4) 9/2))))
(.f64 (exp.f64 -3) (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 9/2) (.f64 x (.f64 x 3)))))
(+.f64 (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 6))) (+.f64 (.f64 3 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 -1) 3) (.f64 9/2 (.f64 (pow.f64 (exp.f64 -1) 3) (pow.f64 x 4))))))
(fma.f64 9/2 (.f64 (pow.f64 x 6) (pow.f64 (exp.f64 -1) 3)) (+.f64 (fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3)) (.f64 9/2 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3)))))
(fma.f64 9/2 (.f64 (pow.f64 x 6) (pow.f64 (exp.f64 -1) 3)) (fma.f64 3 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1) 3)) (fma.f64 9/2 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1) 3)) (pow.f64 (exp.f64 -1) 3))))
(+.f64 (fma.f64 (.f64 x x) (.f64 3 (exp.f64 -3)) (exp.f64 -3)) (.f64 (.f64 (exp.f64 -3) 9/2) (+.f64 (pow.f64 x 4) (pow.f64 x 6))))
(+.f64 (exp.f64 -3) (.f64 (exp.f64 -3) (+.f64 (.f64 x (.f64 x 3)) (.f64 9/2 (+.f64 (pow.f64 x 4) (pow.f64 x 6))))))
(.f64 (exp.f64 -3) (+.f64 (+.f64 1 (.f64 x (.f64 x 3))) (.f64 9/2 (+.f64 (pow.f64 x 4) (pow.f64 x 6)))))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 3)
(exp.f64 (*.f64 3 (fma.f64 x x -1)))

prune75.0ms (5.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	118	2	120

Error

0.0b

Counts

120 → 2

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3)) 3))
✓	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 1707 to 1377 computations (19.3% saved)

regimes41.0ms (3.1%)

Accuracy

Total 0.0b remaining (1.7%)

Threshold costs 0.0b (1.7%)

Counts

19 → 1

Compiler

Compiled 222 to 168 computations (24.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7

Stop Event

1×

saturated

Calls

Call 1

Inputs
(exp.f64 (fma.f64 x x -1))

Outputs
(exp.f64 (fma.f64 x x -1))

end42.0ms (3.2%)

Stop Event

1×

done

Compiler

Compiled 30 to 22 computations (26.7% saved)

Details

analyze5.0ms (0.4%)

sample788.0ms (59.3%)

preprocess29.0ms (2.2%)

simplify19.0ms (1.4%)

prune2.0ms (0.2%)

localize4.0ms (0.3%)

series1.0ms (0.1%)

rewrite33.0ms (2.5%)

simplify38.0ms (2.9%)

prune16.0ms (1.2%)

localize6.0ms (0.4%)

series6.0ms (0.4%)

rewrite39.0ms (2.9%)

simplify44.0ms (3.3%)

prune54.0ms (4.1%)

localize9.0ms (0.7%)

series2.0ms (0.1%)

rewrite37.0ms (2.8%)

simplify39.0ms (2.9%)

prune75.0ms (5.6%)

regimes41.0ms (3.1%)

simplify2.0ms (0.1%)

end42.0ms (3.2%)

Profiling