Details

analyze1.5s (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample307.0ms (2%)

Algorithm

1×

intervals

Results

81.0ms	125×	body	1024	valid
77.0ms	125×	body	1024	nan
37.0ms	29×	body	256	valid
31.0ms	77×	body	512	nan
30.0ms	61×	body	512	valid
19.0ms	15×	body	2048	valid
9.0ms	27×	body	256	nan
4.0ms	26×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

520×	`sub-neg_binary64`
373×	`div-sub_binary64`
267×	`log-prod_binary64`
240×	`associate-/r*_binary64`
225×	`sqr-pow_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	292	55
4	689	55
5	1392	55
6	3381	55
7	4578	55
8	4212	55
9	4795	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

60.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))

Status

Error

Program

▶

60.0b

(*.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))

Compiler

Compiled 99 to 72 computations (27.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
1.5b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
5.1b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite488.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

59.8b

Rules

66×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`

Counts

4 → 127

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
5.0ms	(*.f64 (/.f64 PI.f64 4) f)
5.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 5197 to 3460 computations (33.4% saved)

series53.0ms (0.4%)

Error

2.3b

Counts

4 → 12

Calls

4 calls:

21.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
12.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 PI.f64 f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1067 to 805 computations (24.6% saved)

simplify234.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

476×	`times-frac_binary64`
299×	`*-commutative_binary64`
292×	`associate-/l*_binary64`
261×	`exp-prod_binary64`
236×	`associate-*l/_binary64`

Counts

139 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	5947
1	540	5597
2	1416	5586
3	2991	5573
4	4698	5573
5	4949	5573

prune49.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	5	70

Error

2.3b

Counts

70 → 5

Alt Table

Status	Error	Program
	59.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2)) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) 3)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (+.f64 (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2) (exp.f64 (+.f64 (.f64 (/.f64 PI.f64 4) f) (.f64 f (*.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
	3.5b	(*.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (/.f64 4 f) PI.f64)))
▶	3.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
✓	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))

Compiler

Compiled 2045 to 1376 computations (32.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
1.5b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))

rewrite371.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

34×	`add-sqr-sqrt_binary64`
33×	`add-exp-log_binary64`
30×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 113

Calls

4 calls:

9.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
8.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
7.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
5.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 3782 to 2552 computations (32.5% saved)

series159.0ms (1%)

Error

2.1b

Counts

4 → 12

Calls

4 calls:

97.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
31.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
13.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 809 to 620 computations (23.4% saved)

simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-rgt-in_binary64`
405×	`distribute-lft-in_binary64`
247×	`associate-/l/_binary64`
202×	`associate-l_binary64`
163×	`associate-r_binary64`

Counts

125 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4787
1	619	4102
2	2110	4073
3	4688	4073
4	4999	4073

prune199.0ms (1.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	94	12	106
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	95	16	111

Error

1.9b

Counts

111 → 16

Alt Table

Status	Error	Program
	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) 3)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (+.f64 (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2) (exp.f64 (+.f64 (.f64 (/.f64 PI.f64 4) f) (.f64 f (*.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
	3.5b	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))))) (log.f64 f)) (log.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	3.5b	(*.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (/.f64 4 f) PI.f64)))
	3.7b	(.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	4.7b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (*.f64 (cbrt.f64 (/.f64 -4 PI.f64)) (cbrt.f64 (/.f64 -4 PI.f64)))) (cbrt.f64 (/.f64 -4 PI.f64)))
	3.7b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))))
	3.8b	(cbrt.f64 (/.f64 -64 (pow.f64 (/.f64 PI.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) 3)))
	4.2b	(.f64 (exp.f64 (log.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
✓	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	59.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2)) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))))) (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))))))
	3.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.8b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) 3)) (/.f64 -4 PI.f64))
	3.5b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (log.f64 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	3.6b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) (sqrt.f64 PI.f64)) (/.f64 -4 (sqrt.f64 PI.f64)))
▶	3.4b	(/.f64 (.f64 -4 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2))))) PI.f64)

Compiler

Compiled 3885 to 2707 computations (30.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))
0.3b	(/.f64 (.f64 -4 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2))))) PI.f64)
1.5b	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))

rewrite224.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

30×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
18×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

12.0ms	(/.f64 (.f64 -4 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2))))) PI.f64)
9.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))
9.0ms	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 2904 to 1939 computations (33.2% saved)

series85.0ms (0.6%)

Error

1.9b

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (.f64 -4 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2))))) PI.f64)
26.0ms	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))
13.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))
8.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 809 to 620 computations (23.4% saved)

simplify94.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

804×	`associate-/l*_binary64`
343×	`associate-/l/_binary64`
319×	`distribute-rgt-in_binary64`
301×	`distribute-lft-in_binary64`
174×	`associate-/r/_binary64`

Counts

99 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	3958
1	509	3303
2	1826	3264
3	4995	3264

prune106.0ms (0.7%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	75	16	91

Error

1.9b

Counts

91 → 16

Alt Table

Status	Error	Program
	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) 3)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (+.f64 (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2) (exp.f64 (+.f64 (.f64 (/.f64 PI.f64 4) f) (.f64 f (*.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
▶	3.5b	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))))) (log.f64 f)) (log.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	3.5b	(*.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (/.f64 4 f) PI.f64)))
	3.7b	(.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	4.7b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (*.f64 (cbrt.f64 (/.f64 -4 PI.f64)) (cbrt.f64 (/.f64 -4 PI.f64)))) (cbrt.f64 (/.f64 -4 PI.f64)))
	3.7b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))))
	3.8b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f)))) (/.f64 -4 PI.f64)) 3))
	4.2b	(.f64 (exp.f64 (log.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
✓	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	59.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2)) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))))) (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))))))
	3.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.8b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) 3)) (/.f64 -4 PI.f64))
	3.5b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (log.f64 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	3.6b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) (sqrt.f64 PI.f64)) (/.f64 -4 (sqrt.f64 PI.f64)))
✓	3.4b	(/.f64 (.f64 -4 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2))))) PI.f64)

Compiler

Compiled 2900 to 1931 computations (33.4% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))))
1.2b	(cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))))
1.2b	(log.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (*.f64 PI.f64 1/2)))
1.3b	(log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))))

rewrite240.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

19×	`*-un-lft-identity_binary64`
18×	`log-prod_binary64`
16×	`cbrt-prod_binary64`
11×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`

Counts

4 → 70

Calls

4 calls:

7.0ms	(log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))))
6.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (*.f64 PI.f64 1/2)))
5.0ms	(cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))))
5.0ms	(cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))))

Compiler

Compiled 3699 to 2560 computations (30.8% saved)

series132.0ms (0.9%)

Error

1.7b

Counts

4 → 12

Calls

4 calls:

44.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (*.f64 PI.f64 1/2)))
31.0ms	(log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))))
23.0ms	(cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))))
22.0ms	(cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))))

Compiler

Compiled 1377 to 1088 computations (21% saved)

simplify142.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

486×	`distribute-rgt-in_binary64`
444×	`distribute-lft-in_binary64`
241×	`log-prod_binary64`
225×	`sub-neg_binary64`
206×	`cancel-sign-sub-inv_binary64`

Counts

82 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	3804
1	298	3551
2	690	3471
3	1934	3437
4	4824	3437
5	4948	3437

prune136.0ms (0.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	2	11	13
Picked	1	0	1
Done	0	2	2
Total	70	14	84

Error

1.7b

Counts

84 → 14

Alt Table

Status	Error	Program
	59.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (sqrt.f64 (exp.f64 PI.f64)) f) (pow.f64 (exp.f64 (.f64 PI.f64 f)) -1/2)) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	2.7b	(.f64 (/.f64 -4 PI.f64) (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))))) (log.f64 f)) (log.f64 (/.f64 (pow.f64 2 4/3) PI.f64))))
	3.5b	(*.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (/.f64 4 f) PI.f64)))
	3.7b	(.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.7b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))))
	3.8b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f)))) (/.f64 -4 PI.f64)) 3))
	4.2b	(.f64 (exp.f64 (log.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
✓	60.0b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))))) (cbrt.f64 (.f64 (/.f64 -4 PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))))))
	3.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.8b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) 3)) (/.f64 -4 PI.f64))
	3.5b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (log.f64 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	3.6b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) (sqrt.f64 PI.f64)) (/.f64 -4 (sqrt.f64 PI.f64)))
✓	3.4b	(/.f64 (.f64 -4 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2))))) PI.f64)

Compiler

Compiled 3447 to 2414 computations (30% saved)

regimes1.3s (8.4%)

Accuracy

Total 0.8b remaining (35.9%)

Threshold costs 0.8b (35.9%)

Compiler

Compiled 35490 to 26126 computations (26.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	34	53
2	39	53
3	41	53
4	42	53
5	42	53

end1.0ms (0%)

Compiler: Compiled 32 to 26 computations (18.8% saved)

sample9.1s (59.9%)

Algorithm

1×

intervals

Results

2.6s	3947×	body	1024	valid
2.4s	3947×	body	1024	nan
917.0ms	2017×	body	512	nan
883.0ms	1914×	body	512	valid
721.0ms	475×	body	2048	valid
308.0ms	984×	body	256	valid
287.0ms	983×	body	256	nan
165.0ms	680×	body	128	valid
5.0ms	3×	body	2048	nan
1.0ms	4×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 581 to 435 computations (25.1% saved)

Details

analyze1.5s (9.8%)

sample307.0ms (2%)

simplify76.0ms (0.5%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite488.0ms (3.2%)

series53.0ms (0.4%)

simplify234.0ms (1.5%)

prune49.0ms (0.3%)

localize19.0ms (0.1%)

rewrite371.0ms (2.4%)

series159.0ms (1%)

simplify144.0ms (0.9%)

prune199.0ms (1.3%)

localize19.0ms (0.1%)

rewrite224.0ms (1.5%)

series85.0ms (0.6%)

simplify94.0ms (0.6%)

prune106.0ms (0.7%)

localize28.0ms (0.2%)

rewrite240.0ms (1.6%)

series132.0ms (0.9%)

simplify142.0ms (0.9%)

prune136.0ms (0.9%)

regimes1.3s (8.4%)

simplify4.0ms (0%)

end1.0ms (0%)

sample9.1s (59.9%)

Profiling