Details

analyze1.4s (8.8%)

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)

sample314.0ms (1.9%)

Algorithm

1×

intervals

Results

123.0ms	116×	body	1024	valid
66.0ms	104×	body	1024	nan
32.0ms	69×	body	512	valid
30.0ms	69×	body	512	nan
24.0ms	16×	body	2048	valid
10.0ms	31×	body	256	valid
8.0ms	28×	body	256	nan
5.0ms	24×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
569×	`fma-def_binary64`
365×	`div-sub_binary64`
240×	`associate-/r*_binary64`
202×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	295	55
4	736	55
5	1625	55
6	4003	55
7	5053	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

60.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	60.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (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

▶

60.5b

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

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
1.2b	(/.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))))
6.4b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite683.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

60.4b

Rules

41×	`add-cube-cbrt_binary64`
30×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 172

Calls

4 calls:

114.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
42.0ms	(*.f64 PI.f64 f)
24.0ms	(/.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))))
16.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 7074 to 4747 computations (32.9% saved)

series51.0ms (0.3%)

Error

2.0b

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.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))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
6.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 1067 to 805 computations (24.6% saved)

simplify166.0ms (1%)

Algorithm

1×	egg-herbie

Rules

619×	`times-frac_binary64`
520×	`fma-def_binary64`
266×	`fma-neg_binary64`
244×	`unswap-sqr_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

184 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	5443
1	512	4808
2	1825	4323
3	4728	4323
4	4920	4323

prune114.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Error

1.9b

Counts

119 → 7

Alt Table

Status	Error	Program
✓	60.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
▶	3.1b	(.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))
	60.5b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))) 3))) (/.f64 -4 PI.f64))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))))))) (/.f64 -4 PI.f64))
	60.7b	(.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 f) (.f64 PI.f64 1/2)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))))) (/.f64 -4 PI.f64))

Compiler

Compiled 4467 to 3036 computations (32% saved)

localize18.0ms (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))
1.2b	(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))))

rewrite408.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

34×	`pow1_binary64`
32×	`add-exp-log_binary64`
28×	`add-cube-cbrt_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 180

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 f (.f64 PI.f64 1/2)))
16.0ms	(*.f64 (/.f64 PI.f64 4) f)
16.0ms	(.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))
12.0ms	(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))))

Compiler

Compiled 5543 to 3795 computations (31.5% saved)

series75.0ms (0.5%)

Error

1.7b

Counts

4 → 12

Calls

4 calls:

26.0ms	(.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))
22.0ms	(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))))
11.0ms	(/.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)

simplify161.0ms (1%)

Algorithm

1×	egg-herbie

Rules

432×	`distribute-rgt-in_binary64`
408×	`distribute-lft-in_binary64`
270×	`fma-def_binary64`
181×	`unswap-sqr_binary64`
173×	`associate-l_binary64`

Counts

192 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	6107
1	572	5234
2	2059	4859
3	5152	4859

prune163.0ms (1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	108	11	119
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	110	16	126

Error

1.5b

Counts

126 → 16

Alt Table

Status	Error	Program
▶	3.1b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) PI.f64) -4)
	3.2b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.8b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) (/.f64 -4 PI.f64))
	3.1b	(/.f64 1 (/.f64 (/.f64 PI.f64 -4) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))))))) (/.f64 -4 PI.f64))
	60.5b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))) 3))) (/.f64 -4 PI.f64))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	4.0b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))) (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64)))) (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))))
✓	60.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	13.5b	(log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))) (/.f64 -4 PI.f64)))
	3.2b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	3.4b	(.f64 (/.f64 (+.f64 (.f64 8 (pow.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) 3)) (pow.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) 3)) (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) (.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) 1))) (/.f64 -4 PI.f64))
	3.3b	(.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) 3) (pow.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2))) 3)) (fma.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2))) (log.f64 (.f64 f (.f64 PI.f64 1/2))) (.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (.f64 f (*.f64 PI.f64 1/2))))))) (/.f64 -4 PI.f64))
	60.7b	(.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 f) (.f64 PI.f64 1/2)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	3.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) 2)) (cbrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))

Compiler

Compiled 4408 to 2960 computations (32.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))
0.3b	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) PI.f64)
1.2b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))

rewrite352.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

35×	`add-cube-cbrt_binary64`
31×	`pow1_binary64`
28×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

4 → 180

Calls

4 calls:

22.0ms	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))
15.0ms	(*.f64 PI.f64 f)
15.0ms	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) PI.f64)
12.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))

Compiler

Compiled 5680 to 3585 computations (36.9% saved)

series76.0ms (0.5%)

Error

1.5b

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) PI.f64)
22.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))
12.0ms	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))
6.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 738 to 569 computations (22.9% saved)

simplify179.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-def_binary64`
171×	`fma-neg_binary64`
169×	`div-sub_binary64`
152×	`associate-/r*_binary64`
149×	`associate-l_binary64`

Counts

192 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	6274
1	560	5551
2	2309	5035
3	4633	5033
4	5187	5033

prune94.0ms (0.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	73	14	87

Error

1.5b

Counts

87 → 14

Alt Table

Status	Error	Program
▶	3.1b	(.f64 (/.f64 (.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))) (pow.f64 PI.f64 2)) -4)
	3.2b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.1b	(/.f64 1 (/.f64 (/.f64 PI.f64 -4) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))))))) (/.f64 -4 PI.f64))
	60.5b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))) 3))) (/.f64 -4 PI.f64))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (+.f64 (/.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) PI.f64) (/.f64 (neg.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2)))) PI.f64)) -4)
	3.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) 2)) (cbrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
✓	60.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	13.5b	(log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))) (/.f64 -4 PI.f64)))
	3.8b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.1b	(.f64 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64) -4)
	3.3b	(.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) 3) (pow.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2))) 3)) (fma.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2))) (log.f64 (.f64 f (.f64 PI.f64 1/2))) (.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (.f64 f (*.f64 PI.f64 1/2))))))) (/.f64 -4 PI.f64))
	60.7b	(.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 f) (.f64 PI.f64 1/2)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))))) (/.f64 -4 PI.f64))

Compiler

Compiled 2786 to 1872 computations (32.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))
0.3b	(.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))
0.4b	(/.f64 (.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (pow.f64 PI.f64 2))
1.2b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))

rewrite311.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

42×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`
27×	`pow1_binary64`
22×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

4 → 187

Calls

4 calls:

22.0ms	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))
16.0ms	(.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))
16.0ms	(/.f64 (.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (pow.f64 PI.f64 2))
12.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))

Compiler

Compiled 7226 to 4666 computations (35.4% saved)

series122.0ms (0.7%)

Error

1.5b

Counts

4 → 15

Calls

4 calls:

46.0ms	(.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))
24.0ms	(/.f64 (.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (pow.f64 PI.f64 2))
22.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))
13.0ms	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))

Compiler

Compiled 1382 to 1089 computations (21.2% saved)

simplify247.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

327×	`fma-neg_binary64`
318×	`associate-r_binary64`
296×	`associate-l_binary64`
192×	`unswap-sqr_binary64`
161×	`fma-def_binary64`

Counts

202 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	8829
1	820	7368
2	3293	6540
3	4962	6540
4	5012	6540

prune107.0ms (0.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	93	14	107

Error

1.5b

Counts

107 → 14

Alt Table

Status	Error	Program
	3.1b	(/.f64 1 (/.f64 (/.f64 PI.f64 -4) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))))))) (/.f64 -4 PI.f64))
	60.5b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (-.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))) 3))) (/.f64 -4 PI.f64))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)))) (cbrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	4.1b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (cbrt.f64 PI.f64))) (pow.f64 PI.f64 2)) -4)
	60.7b	(.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 f) (.f64 PI.f64 1/2)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (*.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (+.f64 (/.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) PI.f64) (/.f64 (neg.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2)))) PI.f64)) -4)
	3.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) 2)) (cbrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.1b	(.f64 (.f64 (.f64 PI.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (pow.f64 PI.f64 -2)) -4)
	60.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	3.1b	(.f64 (/.f64 (.f64 PI.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f)))) (pow.f64 PI.f64 2)) -4)
	3.1b	(.f64 (/.f64 (+.f64 (.f64 (.f64 f (pow.f64 PI.f64 2)) -1/8) (+.f64 (.f64 1/8 (.f64 f (pow.f64 PI.f64 2))) (.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))))) (pow.f64 PI.f64 2)) -4)
	3.3b	(.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) 3) (pow.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2))) 3)) (fma.f64 (log.f64 (.f64 f (.f64 PI.f64 1/2))) (log.f64 (.f64 f (.f64 PI.f64 1/2))) (.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (log.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (.f64 f (*.f64 PI.f64 1/2))))))) (/.f64 -4 PI.f64))

Compiler

Compiled 3275 to 2186 computations (33.3% saved)

regimes2.1s (12.9%)

Accuracy

Total 0.3b remaining (17.3%)

Threshold costs 0.3b (17.3%)

Compiler

Compiled 54120 to 39242 computations (27.5% saved)

bsearch16.0ms (0.1%)

Compiler: Compiled 30 to 23 computations (23.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`*-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	132
1	58	132
2	77	132
3	90	132
4	97	132
5	98	132
6	97	132

end2.0ms (0%)

Compiler: Compiled 78 to 57 computations (26.9% saved)

sample9.1s (55.3%)

Algorithm

1×

intervals

Results

2.7s	3884×	body	1024	valid
2.4s	3746×	body	1024	nan
992.0ms	1977×	body	512	valid
832.0ms	1797×	body	512	nan
645.0ms	517×	body	2048	valid
331.0ms	990×	body	256	valid
302.0ms	940×	body	256	nan
110.0ms	632×	body	128	valid
1.0ms	3×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 669 to 489 computations (26.9% saved)

Details

analyze1.4s (8.8%)

sample314.0ms (1.9%)

simplify53.0ms (0.3%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite683.0ms (4.2%)

series51.0ms (0.3%)

simplify166.0ms (1%)

prune114.0ms (0.7%)

localize18.0ms (0.1%)

rewrite408.0ms (2.5%)

series75.0ms (0.5%)

simplify161.0ms (1%)

prune163.0ms (1%)

localize18.0ms (0.1%)

rewrite352.0ms (2.1%)

series76.0ms (0.5%)

simplify179.0ms (1.1%)

prune94.0ms (0.6%)

localize20.0ms (0.1%)

rewrite311.0ms (1.9%)

series122.0ms (0.7%)

simplify247.0ms (1.5%)

prune107.0ms (0.7%)

regimes2.1s (12.9%)

bsearch16.0ms (0.1%)

simplify7.0ms (0%)

end2.0ms (0%)

sample9.1s (55.3%)

Profiling