Details

analyze808.0ms (19.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
12.5%	62.5%	25%	4
18.7%	43.7%	37.5%	5
21.9%	34.4%	43.8%	6
23.4%	29.7%	46.9%	7
24.2%	27.3%	48.5%	8
24.6%	26.2%	49.2%	9
24.8%	25.6%	49.6%	10
24.9%	25.3%	49.8%	11
24.9%	25.1%	49.9%	12
25%	25.1%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.9s (71.2%)

Results

1.5s	8256×	body	128	valid
1.3s	8226×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess65.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

prune4.0ms (0.1%)

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

33.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize11.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	31.1b	(sqrt.f64 (fma.f64 x x -1))

series5.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(sqrt.f64 (fma.f64 x x -1))
1.0ms	x	@	-inf	(sqrt.f64 (fma.f64 x x -1))
1.0ms	x	@	inf	(sqrt.f64 (fma.f64 x x -1))

rewrite50.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

399×	`pow1_binary64`
369×	`add-log-exp_binary64`
369×	`log1p-expm1-u_binary64`
369×	`expm1-log1p-u_binary64`
360×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	94	7
2	1010	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x -1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x -1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))))

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

734×	`associate-/l*_binary64`
483×	`associate-/r*_binary64`
433×	`fma-def_binary64`
279×	`associate-*l/_binary64`
220×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	203
1	138	193
2	375	191
3	1355	185

Stop Event

1×	node limit

Counts

32 → 42

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(-.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))) x)
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))) x)

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) (sqrt.f64 -1))
(-.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))))
(+.f64 (sqrt.f64 -1) (-.f64 (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)))))
(-.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (.f64 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (-.f64 1/2 (/.f64 (.f64 x x) -8))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))))
(+.f64 (sqrt.f64 -1) (-.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (/.f64 (.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5))) (-.f64 (sqrt.f64 -1) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (.f64 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (-.f64 1/2 (/.f64 (.f64 x x) -8)))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (/.f64 1/2 x))
(+.f64 x (/.f64 -1/2 x))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(-.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
(-.f64 x (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(-.f64 (-.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5)))
(+.f64 (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (+.f64 x (/.f64 -1/16 (pow.f64 x 5))))
(*.f64 -1 x)
(neg.f64 x)
(-.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (/.f64 1/2 x) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))) x)
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))) x)
(+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x)))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))) (-.f64 (/.f64 1/16 (pow.f64 x 5)) x))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 1/16 (pow.f64 x 5)) x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x)))

prune44.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Alt Table

Status	Error	Program
✓	33.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶	0.3b	(log.f64 (+.f64 x x))

Compiler

Compiled 609 to 452 computations (25.8% saved)

localize6.0ms (0.1%)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
✓	33.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.3b	(log.f64 (+.f64 x x))

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes39.0ms (1%)

Accuracy

Total 0.6b remaining (84.2%)

Threshold costs 0.6b (84.2%)

Counts

4 → 1

Compiler

Compiled 132 to 91 computations (31.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x x))

end63.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 24 to 15 computations (37.5% saved)

Details

analyze808.0ms (19.8%)

sample2.9s (71.2%)

preprocess65.0ms (1.6%)

simplify43.0ms (1%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

series5.0ms (0.1%)

rewrite50.0ms (1.2%)

simplify36.0ms (0.9%)

prune44.0ms (1.1%)

localize6.0ms (0.1%)

prune2.0ms (0%)

regimes39.0ms (1%)

simplify3.0ms (0.1%)

end63.0ms (1.5%)

Profiling