Details

analyze1.4s (9.4%)

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)

sample10.5s (68.8%)

Results

3.3s	4074×	body	1024	valid
3.1s	4092×	body	1024	invalid
1.2s	2005×	body	512	valid
1.1s	2018×	body	512	invalid
796.0ms	525×	body	2048	valid
451.0ms	1013×	body	256	valid
401.0ms	995×	body	256	invalid
148.0ms	639×	body	128	valid
5.0ms	5×	body	2048	invalid
1.0ms	5×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
323×	`fma-neg_binary64`
202×	`distribute-rgt-in_binary64`
192×	`cancel-sign-sub-inv_binary64`
175×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	122	59
3	326	55
4	975	55
5	2553	55

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.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 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.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
✓	0.1b	(pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f)
✓	0.2b	(*.f64 (PI.f64) f)
✓	0.5b	(/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
✓	6.0b	(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))

series50.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

34.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
9.0ms	(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))
4.0ms	(*.f64 (PI.f64) f)
3.0ms	(pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f)

rewrite90.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

716×	`prod-diff_binary64`
158×	`egg-rr`
154×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	83
1	317	83
2	4279	83

Stop Event

1×	node limit

Counts

4 → 158

Calls

4 calls:

86.0ms	(pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f)
86.0ms	(*.f64 (PI.f64) f)
86.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
86.0ms	(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
401×	`cancel-sign-sub-inv_binary64`
339×	`associate-l_binary64`
325×	`fma-def_binary64`
320×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	984
1	191	972
2	577	968
3	2435	964
4	4725	964

Stop Event

1×	node limit

Counts

206 → 187

prune214.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	226	4	230

Error

1.3b

Counts

230 → 4

Alt Table

Status	Error	Program
✓	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
▶	1.5b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/192 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 10576 to 6781 computations (35.9% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/192 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
✓	1.0b	(pow.f64 (PI.f64) 3)
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	1.6b	(pow.f64 (PI.f64) 7)

series77.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/192 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
0.0ms	(pow.f64 (PI.f64) 7)
0.0ms	(pow.f64 (PI.f64) 5)
0.0ms	(pow.f64 (PI.f64) 3)

rewrite45.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

337×	`log1p-expm1-u_binary64`
337×	`expm1-log1p-u_binary64`
326×	`add-cbrt-cube_binary64`
325×	`add-log-exp_binary64`
322×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	82
1	766	82

Stop Event

1×	node limit

Counts

4 → 64

Calls

4 calls:

44.0ms	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/192 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
44.0ms	(pow.f64 (PI.f64) 3)
44.0ms	(pow.f64 (PI.f64) 5)
44.0ms	(pow.f64 (PI.f64) 7)

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

364×	`cancel-sign-sub-inv_binary64`
226×	`unswap-sqr_binary64`
165×	`distribute-rgt-in_binary64`
162×	`sub-neg_binary64`
156×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	3236
1	560	3157
2	2557	2615

Stop Event

1×	node limit

Counts

76 → 87

prune204.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	80	11	91

Error

1.1b

Counts

91 → 11

Alt Table

Status	Error	Program
✓	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
▶	1.5b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) (/.f64 -4 (PI.f64)))
	1.6b	(.f64 (-.f64 (fma.f64 1/48 (.f64 f (.f64 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)))
	2.3b	(.f64 (exp.f64 (log.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))))) (/.f64 -4 (PI.f64)))
	1.8b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) 3)) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (pow.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7)))))))) 2) (/.f64 -4 (PI.f64)))
	2.4b	(.f64 (pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) 3) 1/3) (/.f64 -4 (PI.f64)))
	2.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7)))))))) 2) (cbrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7))))))))) (/.f64 -4 (PI.f64)))
	2.2b	(.f64 (-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))))) 1) (/.f64 -4 (PI.f64)))

Compiler

Compiled 8171 to 5402 computations (33.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) (/.f64 -4 (PI.f64)))
✓	0.5b	(log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))
✓	1.0b	(exp.f64 (PI.f64))
✓	1.0b	(pow.f64 (exp.f64 (PI.f64)) 1/4)

series377.0ms (2.5%)

Counts

4 → 24

Calls

4 calls:

332.0ms	(log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))
44.0ms	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) (/.f64 -4 (PI.f64)))
0.0ms	(pow.f64 (exp.f64 (PI.f64)) 1/4)
0.0ms	(exp.f64 (PI.f64))

rewrite41.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

327×	`log1p-expm1-u_binary64`
327×	`expm1-log1p-u_binary64`
320×	`add-cbrt-cube_binary64`
317×	`add-log-exp_binary64`
314×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	109
1	709	109

Stop Event

1×	node limit

Counts

4 → 62

Calls

4 calls:

40.0ms	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) (/.f64 -4 (PI.f64)))
40.0ms	(log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))
40.0ms	(exp.f64 (PI.f64))
40.0ms	(pow.f64 (exp.f64 (PI.f64)) 1/4)

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

384×	`fma-def_binary64`
372×	`associate-r_binary64`
368×	`associate-l_binary64`
267×	`associate--r+_binary64`
234×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1164
1	418	1148
2	1368	1139

Stop Event

1×	node limit

Counts

86 → 95

prune183.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	93	13	106

Error

1.0b

Counts

106 → 13

Alt Table

Status	Error	Program
✓	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
	10.6b	(log.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7)))))) (/.f64 -4 (PI.f64))))
	1.6b	(.f64 (-.f64 (fma.f64 1/48 (.f64 f (.f64 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)))
	1.7b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
✓	1.5b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) (/.f64 -4 (PI.f64)))
▶	1.5b	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7))))))) -4) (PI.f64))
	1.9b	(-.f64 (fma.f64 4 (+.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (.f64 (PI.f64) 1/2)) (PI.f64))) (.f64 (pow.f64 f 4) (.f64 7/5760 (pow.f64 (PI.f64) 3)))) (fma.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 f 6) 31/1451520) (fma.f64 (.f64 f f) (.f64 (PI.f64) 1/12) (*.f64 4 (/.f64 (log.f64 2) (PI.f64))))))
	1.7b	(.f64 (pow.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7)))))))) 2) (/.f64 -4 (PI.f64)))
	2.4b	(.f64 (pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) 3) 1/3) (/.f64 -4 (PI.f64)))
	2.1b	(/.f64 -4 (/.f64 (PI.f64) (-.f64 (-.f64 (log.f64 2) (log.f64 f)) (log.f64 (*.f64 (PI.f64) 1/2)))))
	2.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7)))))))) 2) (cbrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7))))))))) (/.f64 -4 (PI.f64)))
	2.2b	(.f64 (-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))))) 1) (/.f64 -4 (PI.f64)))

Compiler

Compiled 5717 to 3689 computations (35.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 (PI.f64) f) 3)
✓	0.3b	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7))))))) -4) (PI.f64))
✓	0.5b	(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7)))))))
	1.0b	(exp.f64 (PI.f64))

series205.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

125.0ms

(/.f64 (*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (*.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (*.f64 (PI.f64) f) 3) (fma.f64 1/2 (*.f64 (PI.f64) f) (*.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) -4) (PI.f64))

72.0ms

(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (*.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (*.f64 (PI.f64) f) 3) (fma.f64 1/2 (*.f64 (PI.f64) f) (*.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7)))))))

6.0ms

(pow.f64 (*.f64 (PI.f64) f) 3)

rewrite45.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

312×	`log1p-expm1-u_binary64`
312×	`expm1-log1p-u_binary64`
307×	`add-cbrt-cube_binary64`
306×	`add-log-exp_binary64`
303×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	149
1	681	149

Stop Event

1×	node limit

Counts

3 → 55

Calls

3 calls:

43.0ms

(pow.f64 (*.f64 (PI.f64) f) 3)

43.0ms

(/.f64 (*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (*.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (*.f64 (PI.f64) f) 3) (fma.f64 1/2 (*.f64 (PI.f64) f) (*.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) -4) (PI.f64))

43.0ms

(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 1/4 f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (*.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (*.f64 (PI.f64) f) 3) (fma.f64 1/2 (*.f64 (PI.f64) f) (*.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7)))))))

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
293×	`associate-/r*_binary64`
261×	`associate-+r+_binary64`
241×	`fma-neg_binary64`
234×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	296	6716
1	1045	6565
2	4918	6565

Stop Event

1×	node limit

Counts

91 → 102

prune280.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	4	6	10
Picked	1	0	1
Done	0	2	2
Total	122	9	131

Error

1.0b

Counts

131 → 9

Alt Table

Status	Error	Program
✓	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	60.9b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))) 2))) (/.f64 -4 (PI.f64)))
	1.6b	(-.f64 (fma.f64 4 (/.f64 (log.f64 f) (PI.f64)) (.f64 (pow.f64 f 4) (.f64 (pow.f64 (PI.f64) 3) 7/5760))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 (.f64 f f) (*.f64 (PI.f64) 1/12))))
	2.4b	(.f64 (pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) 3) 1/3) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
✓	1.5b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (*.f64 (PI.f64) f) 7))))))) (/.f64 -4 (PI.f64)))
	1.9b	(-.f64 (fma.f64 4 (+.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (.f64 (PI.f64) 1/2)) (PI.f64))) (.f64 (pow.f64 f 4) (.f64 7/5760 (pow.f64 (PI.f64) 3)))) (fma.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 f 6) 31/1451520) (fma.f64 (.f64 f f) (.f64 (PI.f64) 1/12) (*.f64 4 (/.f64 (log.f64 2) (PI.f64))))))
	2.1b	(/.f64 -4 (/.f64 (PI.f64) (-.f64 (-.f64 (log.f64 2) (log.f64 f)) (log.f64 (*.f64 (PI.f64) 1/2)))))
	2.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7)))))))) 2) (cbrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/61440 (pow.f64 (.f64 (PI.f64) f) 5) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (pow.f64 (.f64 (PI.f64) f) 7))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 12097 to 7727 computations (36.1% saved)

regimes852.0ms (5.6%)

Accuracy

Total 0.7b remaining (29.8%)

Threshold costs 0.7b (29.8%)

Counts

103 → 1

Compiler

Compiled 26598 to 18548 computations (30.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	74
1	42	74

Stop Event

1×

saturated

end288.0ms (1.9%)

Compiler: Compiled 459 to 318 computations (30.7% saved)

Details

analyze1.4s (9.4%)

sample10.5s (68.8%)

simplify22.0ms (0.1%)

prune6.0ms (0%)

localize14.0ms (0.1%)

series50.0ms (0.3%)

rewrite90.0ms (0.6%)

simplify54.0ms (0.4%)

prune214.0ms (1.4%)

localize34.0ms (0.2%)

series77.0ms (0.5%)

rewrite45.0ms (0.3%)

simplify57.0ms (0.4%)

prune204.0ms (1.3%)

localize29.0ms (0.2%)

series377.0ms (2.5%)

rewrite41.0ms (0.3%)

simplify36.0ms (0.2%)

prune183.0ms (1.2%)

localize26.0ms (0.2%)

series205.0ms (1.3%)

rewrite45.0ms (0.3%)

simplify108.0ms (0.7%)

prune280.0ms (1.8%)

regimes852.0ms (5.6%)

simplify3.0ms (0%)

end288.0ms (1.9%)

Profiling