Details

analyze1.3s (7.7%)

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)

sample11.5s (69.1%)

Results

3.7s	3987×	body	1024	valid
3.2s	4001×	body	1024	invalid
1.3s	2016×	body	512	valid
1.2s	2039×	body	512	invalid
815.0ms	532×	body	2048	valid
477.0ms	1022×	body	256	invalid
464.0ms	1019×	body	256	valid
200.0ms	702×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify46.0ms (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

prune5.0ms (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

61.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.5b	(.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

▶

61.5b

(*.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 136 to 100 computations (26.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.3b	(*.f64 (PI.f64) 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))))
✓	5.0b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series41.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

29.0ms	(/.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))))
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
2.0ms	(*.f64 (PI.f64) f)

rewrite94.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

617×	`prod-diff_binary64`
152×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
146×	`add-log-exp_binary64`

Counts

4 → 144

Calls

4 calls:

90.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
90.0ms	(*.f64 (PI.f64) f)
90.0ms	(/.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))))
90.0ms	(-.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	14	81
1	311	81
2	4005	81
3	5131	81
0	0	0
1	0	0

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

560×	`cancel-sign-sub-inv_binary64`
495×	`*-commutative_binary64`
455×	`fma-neg_binary64`
445×	`distribute-rgt-neg-in_binary64`
418×	`distribute-lft-neg-in_binary64`

Counts

192 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	924
1	159	918
2	442	914
3	1474	914
4	2580	914
5	4597	914
6	4905	914
7	4926	914

prune179.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	207	4	211

Error

1.9b

Counts

211 → 4

Alt Table

Status	Error	Program
▶	2.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
✓	61.5b	(.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)))
	61.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	61.8b	(.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 (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 9088 to 6103 computations (32.8% 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))))
✓	0.3b	(*.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)))

series32.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

16.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
8.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
6.0ms	(/.f64 4 (*.f64 f (PI.f64)))
2.0ms	(*.f64 f (PI.f64))

rewrite68.0ms (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 → 102

Calls

4 calls:

66.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
66.0ms	(*.f64 f (PI.f64))
66.0ms	(/.f64 4 (*.f64 f (PI.f64)))
66.0ms	(.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

simplify63.0ms (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

126 → 131

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

prune156.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	138	11	149
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	139	14	153

Error

1.5b

Counts

153 → 14

Alt Table

Status	Error	Program
✓	61.5b	(.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)))
	14.6b	(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))))) (log.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))))
	61.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	62.6b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))) 1))
	61.8b	(.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 (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
	2.9b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64))) 3))
	3.0b	(.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64)))
	63.0b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	3.5b	(.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)))
	14.6b	(log.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))
	45.6b	(.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)))
	2.7b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
	2.6b	(-.f64 (.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))) (.f64 1/12 (.f64 (PI.f64) (.f64 f f))))
▶	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)))))

Compiler

Compiled 3892 to 2471 computations (36.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64)))
✓	0.3b	(-.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)))))
✓	0.3b	(/.f64 (log.f64 f) (PI.f64))
✓	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series107.0ms (0.6%)

Counts

4 → 17

Calls

4 calls:

62.0ms	(-.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)))))
31.0ms	(/.f64 (log.f64 f) (PI.f64))
14.0ms	(.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64)))
0.0ms	(log.f64 (/.f64 4 (PI.f64)))

rewrite129.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

954×	`prod-diff_binary64`
193×	`add-sqr-sqrt_binary64`
187×	`egg-rr`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`

Counts

4 → 187

Calls

4 calls:

122.0ms	(.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64)))
122.0ms	(-.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)))))
122.0ms	(/.f64 (log.f64 f) (PI.f64))
122.0ms	(log.f64 (/.f64 4 (PI.f64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	62
1	401	62
2	4855	62
3	6441	62
0	0	0
1	0	0

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

642×	`times-frac_binary64`
445×	`div-sub_binary64`
385×	`fma-def_binary64`
350×	`distribute-rgt-in_binary64`
287×	`distribute-lft-in_binary64`

Counts

204 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	367
1	111	367
2	271	311
3	672	277
4	1929	277
5	3759	277
6	5082	277

prune297.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	190	7	197
Fresh	7	5	12
Picked	1	0	1
Done	0	1	1
Total	198	13	211

Error

1.5b

Counts

211 → 13

Alt Table

Status	Error	Program
▶	2.6b	(-.f64 (.f64 4 (log.f64 (pow.f64 f (/.f64 1 (PI.f64))))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
✓	61.5b	(.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)))
	2.8b	(/.f64 (-.f64 (.f64 64 (pow.f64 (/.f64 (log.f64 f) (PI.f64)) 3)) (pow.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) 3)) (+.f64 (.f64 16 (pow.f64 (/.f64 (log.f64 f) (PI.f64)) 2)) (.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) (+.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) (*.f64 4 (/.f64 (log.f64 f) (PI.f64)))))))
	61.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	62.6b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))) 1))
	61.8b	(.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 (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
	2.9b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64))) 3))
	2.9b	(/.f64 1 (/.f64 (+.f64 (.f64 16 (pow.f64 (/.f64 (log.f64 f) (PI.f64)) 2)) (.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) (+.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) (.f64 4 (/.f64 (log.f64 f) (PI.f64)))))) (-.f64 (.f64 64 (pow.f64 (/.f64 (log.f64 f) (PI.f64)) 3)) (pow.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (*.f64 f f)))) 3))))
	3.5b	(-.f64 (.f64 4 (.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 f)) 2) 1) (/.f64 (cbrt.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)))))
	63.0b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	2.6b	(fma.f64 f (.f64 f (.f64 (PI.f64) -1/12)) (*.f64 4 (/.f64 (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64)))) (PI.f64))))
	2.9b	(-.f64 (.f64 4 (cbrt.f64 (/.f64 (pow.f64 (log.f64 f) 3) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	2.7b	(/.f64 (-.f64 (.f64 (.f64 4 (log.f64 f)) (+.f64 (.f64 1/144 (.f64 (pow.f64 (PI.f64) 2) (pow.f64 f 4))) (.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (-.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 1/12 (.f64 (PI.f64) (.f64 f f))))))) (.f64 (PI.f64) (+.f64 (.f64 1/1728 (pow.f64 (.f64 (PI.f64) (.f64 f f)) 3)) (.f64 64 (pow.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) 3))))) (.f64 (PI.f64) (+.f64 (.f64 1/144 (.f64 (pow.f64 (PI.f64) 2) (pow.f64 f 4))) (.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (-.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 1/12 (.f64 (PI.f64) (.f64 f f))))))))

Compiler

Compiled 11777 to 7420 computations (37% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64)))
✓	0.3b	(-.f64 (.f64 4 (log.f64 (pow.f64 f (/.f64 1 (PI.f64))))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	2.0b	(log.f64 (/.f64 4 (PI.f64)))
✓	5.1b	(pow.f64 f (/.f64 1 (PI.f64)))

series145.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

117.0ms	(-.f64 (.f64 4 (log.f64 (pow.f64 f (/.f64 1 (PI.f64))))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
28.0ms	(pow.f64 f (/.f64 1 (PI.f64)))

rewrite99.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

682×	`prod-diff_binary64`
206×	`add-sqr-sqrt_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
196×	`add-log-exp_binary64`

Counts

2 → 103

Calls

2 calls:

94.0ms	(-.f64 (.f64 4 (log.f64 (pow.f64 f (/.f64 1 (PI.f64))))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
94.0ms	(pow.f64 f (/.f64 1 (PI.f64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	48
1	437	45
2	4709	45
3	5784	45
0	0	0
1	0	0

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

813×	`times-frac_binary64`
376×	`fma-def_binary64`
374×	`distribute-rgt-in_binary64`
309×	`distribute-lft-in_binary64`
259×	`distribute-rgt-neg-in_binary64`

Counts

127 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	486
1	122	477
2	305	459
3	723	419
4	2107	419
5	4218	419
6	5263	419

prune257.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	161	12	173

Error

1.5b

Counts

173 → 12

Alt Table

Status	Error	Program
	2.8b	(/.f64 (-.f64 (.f64 64 (pow.f64 (/.f64 (log.f64 f) (PI.f64)) 3)) (pow.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) 3)) (+.f64 (.f64 16 (pow.f64 (/.f64 (log.f64 f) (PI.f64)) 2)) (.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) (+.f64 (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))) (*.f64 4 (/.f64 (log.f64 f) (PI.f64)))))))
	61.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	62.6b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))) 1))
	61.8b	(.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 (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
	2.9b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64))) 3))
	3.5b	(-.f64 (.f64 4 (.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 f)) 2) 1) (/.f64 (cbrt.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)))))
	63.0b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	2.6b	(fma.f64 f (.f64 f (.f64 (PI.f64) -1/12)) (*.f64 4 (/.f64 (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64)))) (PI.f64))))
	2.9b	(-.f64 (.f64 4 (cbrt.f64 (/.f64 (pow.f64 (log.f64 f) 3) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	2.7b	(/.f64 (-.f64 (.f64 (.f64 4 (log.f64 f)) (+.f64 (.f64 1/144 (.f64 (pow.f64 (PI.f64) 2) (pow.f64 f 4))) (.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (-.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 1/12 (.f64 (PI.f64) (.f64 f f))))))) (.f64 (PI.f64) (+.f64 (.f64 1/1728 (pow.f64 (.f64 (PI.f64) (.f64 f f)) 3)) (.f64 64 (pow.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) 3))))) (.f64 (PI.f64) (+.f64 (.f64 1/144 (.f64 (pow.f64 (PI.f64) 2) (pow.f64 f 4))) (.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (-.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 1/12 (.f64 (PI.f64) (.f64 f f))))))))
✓	61.5b	(.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)))
	2.5b	(-.f64 (.f64 4 (log.f64 (pow.f64 f (/.f64 1 (PI.f64))))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 4 (PI.f64))) 2)) (log.f64 (cbrt.f64 (/.f64 4 (PI.f64))))) (PI.f64)))))

Compiler

Compiled 8941 to 5660 computations (36.7% saved)

regimes1.6s (9.5%)

Accuracy

Total 0.8b remaining (30.1%)

Threshold costs 0.8b (30.1%)

Counts

232 → 1

Compiler

Compiled 46452 to 33824 computations (27.2% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	126
1	49	126
2	66	126
3	92	126
4	110	126
5	126	126
6	140	126
7	147	126
8	149	126
9	146	126

end297.0ms (1.8%)

Compiler: Compiled 584 to 400 computations (31.5% saved)

Iter	Nodes	Cost
0	30	126
1	49	126
2	66	126
3	92	126
4	110	126
5	126	126
6	140	126
7	147	126
8	149	126
9	146	126

Iter	Nodes	Cost
0	30	126
1	49	126
2	66	126
3	92	126
4	110	126
5	126	126
6	140	126
7	147	126
8	149	126
9	146	126

Details

analyze1.3s (7.7%)

sample11.5s (69.1%)

simplify46.0ms (0.3%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series41.0ms (0.2%)

rewrite94.0ms (0.6%)

simplify90.0ms (0.5%)

prune179.0ms (1.1%)

localize10.0ms (0.1%)

series32.0ms (0.2%)

rewrite68.0ms (0.4%)

simplify63.0ms (0.4%)

prune156.0ms (0.9%)

localize14.0ms (0.1%)

series107.0ms (0.6%)

rewrite129.0ms (0.8%)

simplify61.0ms (0.4%)

prune297.0ms (1.8%)

localize18.0ms (0.1%)

series145.0ms (0.9%)

rewrite99.0ms (0.6%)

simplify63.0ms (0.4%)

prune257.0ms (1.5%)

regimes1.6s (9.5%)

simplify8.0ms (0%)

end297.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	30	126
1	49	126
2	66	126
3	92	126
4	110	126
5	126	126
6	140	126
7	147	126
8	149	126
9	146	126