Details

analyze1.3s (7.9%)

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)

sample11.7s (70%)

Results

3.5s	4045×	body	1024	valid
3.4s	4091×	body	1024	invalid
1.5s	2028×	body	512	valid
1.2s	2020×	body	512	invalid
801.0ms	516×	body	2048	valid
445.0ms	995×	body	256	valid
389.0ms	1017×	body	256	invalid
248.0ms	672×	body	128	valid
3.0ms	3×	body	2048	invalid
1.0ms	5×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify47.0ms (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 → 2

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

prune8.0ms (0%)

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

60.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	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))) (-.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

▶

60.9b

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

Compiler

Compiled 136 to 100 computations (26.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (PI.f64) f)
✓	0.3b	(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)))))
✓	1.3b	(/.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))))
✓	6.9b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series448.0ms (2.7%)

Counts

4 → 48

Calls

4 calls:

406.0ms	(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)))))
31.0ms	(/.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))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
2.0ms	(*.f64 (PI.f64) f)

rewrite104.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

618×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
159×	`egg-rr`
154×	`add-log-exp_binary64`
154×	`log1p-expm1-u_binary64`

Counts

4 → 159

Calls

4 calls:

98.0ms	(*.f64 (PI.f64) f)
98.0ms	(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)))))
98.0ms	(/.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))))
98.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	121
1	328	121
2	4187	121
3	5316	121
0	0	0
1	0	0

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

580×	`distribute-rgt-neg-in_binary64`
561×	`distribute-lft-neg-in_binary64`
551×	`fma-neg_binary64`
475×	`associate-r_binary64`
469×	`associate-l_binary64`

Counts

207 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1344
1	241	1338
2	718	1334
3	2998	1334
4	5212	1334

prune220.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	198	6	204
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	199	6	205

Error

2.0b

Counts

205 → 6

Alt Table

Status	Error	Program
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 3))) (/.f64 -4 (PI.f64)))
	61.0b	(.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 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
▶	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (-.f64 (exp.f64 (log1p.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))))))) 1) (/.f64 -4 (PI.f64)))

Compiler

Compiled 10120 to 6849 computations (32.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
✓	0.2b	(*.f64 f (PI.f64))
✓	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.4b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

series33.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

19.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
6.0ms	(/.f64 4 (*.f64 f (PI.f64)))
6.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
2.0ms	(*.f64 f (PI.f64))

rewrite64.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

563×	`log-prod_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
188×	`log-pow_binary64`
128×	`log-div_binary64`

Counts

4 → 106

Calls

4 calls:

62.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
62.0ms	(*.f64 f (PI.f64))
62.0ms	(/.f64 4 (*.f64 f (PI.f64)))
62.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	254	54
2	2936	54
3	5148	54
0	0	0
1	0	0

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
308×	`sub-neg_binary64`
300×	`unswap-sqr_binary64`
266×	`times-frac_binary64`
219×	`fma-def_binary64`

Counts

130 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	750
1	290	723
2	861	714
3	2552	681
4	4778	681
5	4985	681

prune168.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	143	10	153
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	144	15	159

Error

1.7b

Counts

159 → 15

Alt Table

Status	Error	Program
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 3))) (/.f64 -4 (PI.f64)))
	42.5b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (pow.f64 (pow.f64 (/.f64 4 (*.f64 f (PI.f64))) 3) 1/3))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (-.f64 (exp.f64 (log1p.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))))))) 1) (/.f64 -4 (PI.f64)))
	14.1b	(log.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))
	2.6b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	3.4b	(pow.f64 (cbrt.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))) 3)
	61.0b	(.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 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.6b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
▶	2.5b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))
	3.4b	(.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) 2)) (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (exp.f64 (log.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	61.9b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))) 1))
	62.9b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))

Compiler

Compiled 4027 to 2571 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
	0.2b	(*.f64 f (PI.f64))
	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.3b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))

series15.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

15.0ms

(/.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))

rewrite58.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

606×	`log-prod_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
191×	`log-pow_binary64`
170×	`log-div_binary64`

Counts

1 → 44

Calls

1 calls:

57.0ms

(/.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	261	25
2	3163	25
3	5632	25
0	0	0
1	0	0

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
308×	`sub-neg_binary64`
300×	`unswap-sqr_binary64`
264×	`times-frac_binary64`
211×	`fma-def_binary64`

Counts

56 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	564
1	273	555
2	831	546
3	2512	513
4	4758	513
5	4967	513

prune185.0ms (1.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	168	16	184

Error

1.7b

Counts

184 → 16

Alt Table

Status	Error	Program
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 3))) (/.f64 -4 (PI.f64)))
	42.5b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (pow.f64 (pow.f64 (/.f64 4 (*.f64 f (PI.f64))) 3) 1/3))) (/.f64 -4 (PI.f64)))
	2.8b	(.f64 (/.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (PI.f64)) (/.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) -1/4))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (-.f64 (exp.f64 (log1p.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))))))) 1) (/.f64 -4 (PI.f64)))
	14.1b	(log.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))
	2.6b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	3.4b	(pow.f64 (cbrt.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))) 3)
	61.0b	(.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 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
▶	2.6b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
✓	2.5b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))
	2.6b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (exp.f64 (log.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	3.4b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) 2) (PI.f64)) (/.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) -1/4))
	61.9b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))) 1))
	62.9b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))

Compiler

Compiled 4536 to 2877 computations (36.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 f (PI.f64))
	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.3b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
✓	0.3b	(/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4))

series54.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

38.0ms

(/.f64 (PI.f64) (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4))

15.0ms

(/.f64 1 (/.f64 (PI.f64) (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))

rewrite96.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
240×	`prod-diff_binary64`
214×	`log-pow_binary64`
140×	`add-sqr-sqrt_binary64`

Counts

2 → 90

Calls

2 calls:

94.0ms

(/.f64 1 (/.f64 (PI.f64) (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))

94.0ms

(/.f64 (PI.f64) (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	295	50
2	3488	50
3	4899	50
4	5003	50
0	0	0
1	0	0

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
484×	`fma-def_binary64`
295×	`unswap-sqr_binary64`
271×	`cancel-sign-sub-inv_binary64`
215×	`sub-neg_binary64`

Counts

114 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	1816
1	621	1773
2	2312	1769
3	5070	1769

prune241.0ms (1.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	196	4	200
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	200	16	216

Error

1.7b

Counts

216 → 16

Alt Table

Status	Error	Program
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 3))) (/.f64 -4 (PI.f64)))
	2.6b	(/.f64 1 (-.f64 (+.f64 (.f64 1/442368 (/.f64 (.f64 (pow.f64 f 6) (pow.f64 (PI.f64) 7)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 3))) (+.f64 (.f64 1/1327104 (/.f64 (.f64 (pow.f64 f 6) (pow.f64 (PI.f64) 7)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 2))) (+.f64 (.f64 1/192 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 (PI.f64) 3)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 2))) (.f64 1/442368 (/.f64 (.f64 (pow.f64 f 6) (pow.f64 (PI.f64) 7)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 4)))))) (+.f64 (.f64 1/9216 (/.f64 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 5)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 3))) (+.f64 (.f64 1/18432 (/.f64 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 5)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 2))) (*.f64 1/4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))))))))
	42.5b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (pow.f64 (pow.f64 (/.f64 4 (*.f64 f (PI.f64))) 3) 1/3))) (/.f64 -4 (PI.f64)))
	2.8b	(.f64 (/.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (PI.f64)) (/.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) -1/4))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (-.f64 (exp.f64 (log1p.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))))))) 1) (/.f64 -4 (PI.f64)))
	2.6b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 (.f64 f f) (.f64 (PI.f64) 1/12))))
	14.1b	(log.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))
	3.4b	(pow.f64 (cbrt.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))) 3)
	61.0b	(.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 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
✓	2.5b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))
	2.6b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
	2.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (exp.f64 (log.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	3.4b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) 2) (PI.f64)) (/.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) -1/4))
	3.4b	(.f64 (.f64 (/.f64 1 (PI.f64)) (pow.f64 (cbrt.f64 (.f64 (log.f64 (fma.f64 (.f64 (PI.f64) f) 1/12 (/.f64 4 (.f64 (PI.f64) f)))) -4)) 2)) (cbrt.f64 (.f64 (log.f64 (fma.f64 (.f64 (PI.f64) f) 1/12 (/.f64 4 (.f64 (PI.f64) f)))) -4)))
	2.6b	(/.f64 1 (.f64 (PI.f64) (/.f64 -1/4 (log.f64 (fma.f64 (.f64 (PI.f64) f) 1/12 (/.f64 4 (*.f64 (PI.f64) f)))))))

Compiler

Compiled 6298 to 4234 computations (32.8% saved)

regimes1.3s (7.6%)

Accuracy

Total 0.8b remaining (31%)

Threshold costs 0.8b (31%)

Counts

200 → 1

Compiler

Compiled 32196 to 23882 computations (25.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	13	25
2	13	25

end398.0ms (2.4%)

Compiler: Compiled 587 to 425 computations (27.6% saved)

Details

analyze1.3s (7.9%)

sample11.7s (70%)

simplify47.0ms (0.3%)

prune8.0ms (0%)

localize14.0ms (0.1%)

series448.0ms (2.7%)

rewrite104.0ms (0.6%)

simplify60.0ms (0.4%)

prune220.0ms (1.3%)

localize8.0ms (0.1%)

series33.0ms (0.2%)

rewrite64.0ms (0.4%)

simplify64.0ms (0.4%)

prune168.0ms (1%)

localize10.0ms (0.1%)

series15.0ms (0.1%)

rewrite58.0ms (0.3%)

simplify61.0ms (0.4%)

prune185.0ms (1.1%)

localize10.0ms (0.1%)

series54.0ms (0.3%)

rewrite96.0ms (0.6%)

simplify57.0ms (0.3%)

prune241.0ms (1.4%)

regimes1.3s (7.6%)

simplify2.0ms (0%)

end398.0ms (2.4%)

Profiling