Details

analyze1.4s (9.2%)

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)

sample10.6s (72%)

Results

3.4s	4025×	body	1024	valid
3.1s	4032×	body	1024	invalid
1.2s	2035×	body	512	valid
1.1s	1997×	body	512	invalid
768.0ms	535×	body	2048	valid
421.0ms	1028×	body	256	valid
369.0ms	985×	body	256	invalid
140.0ms	633×	body	128	valid
4.0ms	4×	body	2048	invalid
1.0ms	6×	body	128	invalid

Compiler

Compiled 78 to 62 computations (20.5% saved)

preprocess30.0ms (0.2%)

Algorithm

2×	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: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 38 to 30 computations (21.1% saved)

simplify26.0ms (0.2%)

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

prune4.0ms (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

61.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.3b	(.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

▶

61.3b

(*.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	(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)))))
✓	0.3b	(*.f64 (PI.f64) f)
✓	1.0b	(/.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))))
✓	6.2b	(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))

series438.0ms (3%)

Counts

4 → 48

Calls

12 calls:

194.0ms	(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)))))	f	inf
185.0ms	(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)))))	f	-inf
13.0ms	(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)))))	f	0
11.0ms	(/.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))))	f	inf
11.0ms	(/.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))))	f	-inf

rewrite114.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`prod-diff_binary64`
179×	`egg-rr`
162×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	121
1	335	121
2	4471	121

Stop Event

1×	node limit

Counts

4 → 179

simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

580×	`distribute-rgt-neg-in_binary64`
551×	`fma-neg_binary64`
473×	`associate-r_binary64`
468×	`associate-l_binary64`
342×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1344
1	242	1338
2	749	1334
3	3584	1334

Stop Event

1×	node limit

Counts

227 → 207

prune245.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	220	4	224

Error

1.7b

Counts

224 → 4

Alt Table

Status	Error	Program
	2.3b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
▶	2.2b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.3b	(.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))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) 1) (/.f64 -4 (PI.f64)))
	61.3b	(.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) 3)) (/.f64 -4 (PI.f64)))

Compiler

Compiled 11292 to 7183 computations (36.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 f (PI.f64))
✓	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.5b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
✓	1.0b	(*.f64 (PI.f64) 1/12)

series26.0ms (0.2%)

Counts

4 → 12

Calls

9 calls:

8.0ms	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))	f	-inf
5.0ms	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))	f	inf
5.0ms	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))	f	0
2.0ms	(/.f64 4 (*.f64 f (PI.f64)))	f	0
2.0ms	(/.f64 4 (*.f64 f (PI.f64)))	f	inf

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

627×	`log-prod_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
205×	`log-pow_binary64`
146×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	275	43
2	3303	43

Stop Event

1×	node limit

Counts

4 → 87

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
308×	`sub-neg_binary64`
300×	`unswap-sqr_binary64`
200×	`fma-def_binary64`
183×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	564
1	273	555
2	847	546
3	3052	537

Stop Event

1×	node limit

Counts

99 → 110

prune108.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	102	12	114

Error

1.4b

Counts

114 → 12

Alt Table

Status	Error	Program
	62.0b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))) 1))
	2.1b	(-.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)))))
	2.4b	(cbrt.f64 (.f64 (pow.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (*.f64 (PI.f64) f)))) 3) (pow.f64 (/.f64 -4 (PI.f64)) 3)))
	2.3b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	14.1b	(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64)))))) (log.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (*.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))))))
	61.3b	(.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))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) 1) (/.f64 -4 (PI.f64)))
	63.0b	(.f64 -4 (/.f64 (-.f64 (log.f64 (.f64 1/12 (PI.f64))) (log.f64 (/.f64 1 f))) (PI.f64)))
	47.3b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (pow.f64 (pow.f64 (/.f64 4 (*.f64 (PI.f64) f)) 3) 1/3))) (/.f64 -4 (PI.f64)))
	14.6b	(pow.f64 (cbrt.f64 (log.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))))) 3)
	2.1b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (*.f64 (PI.f64) f)))) -4)))
▶	2.0b	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f)))) (*.f64 (PI.f64) -1/4))
	61.3b	(.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) 3)) (/.f64 -4 (PI.f64)))

Compiler

Compiled 2949 to 2025 computations (31.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) f)
✓	0.3b	(/.f64 4 (*.f64 (PI.f64) f))
✓	0.4b	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f)))) (*.f64 (PI.f64) -1/4))
	1.0b	(*.f64 (PI.f64) 1/12)

series23.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

6.0ms	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f)))) (*.f64 (PI.f64) -1/4))	f	-inf
5.0ms	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f)))) (*.f64 (PI.f64) -1/4))	f	0
5.0ms	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f)))) (*.f64 (PI.f64) -1/4))	f	inf
2.0ms	(/.f64 4 (*.f64 (PI.f64) f))	f	-inf
2.0ms	(/.f64 4 (*.f64 (PI.f64) f))	f	0

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

242×	`expm1-udef_binary64`
242×	`log1p-udef_binary64`
207×	`log-pow_binary64`
164×	`prod-diff_binary64`
134×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	277	33
2	3489	33

Stop Event

1×	node limit

Counts

2 → 63

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
309×	`sub-neg_binary64`
300×	`unswap-sqr_binary64`
209×	`fma-def_binary64`
184×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	660
1	278	651
2	851	642
3	3050	633

Stop Event

1×	node limit

Counts

87 → 89

prune134.0ms (0.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Error

1.3b

Counts

133 → 13

Alt Table

Status	Error	Program
	62.0b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))) 1))
	2.1b	(-.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)))))
▶	2.0b	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (*.f64 (PI.f64) -1/4))
	2.3b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	2.3b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	61.3b	(.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))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) 1) (/.f64 -4 (PI.f64)))
	3.0b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) 2) (.f64 (cbrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	61.3b	(.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) 3)) (/.f64 -4 (PI.f64)))
	2.3b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f)))) 3) (pow.f64 (*.f64 (PI.f64) -1/4) 3)))
	47.3b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (pow.f64 (pow.f64 (/.f64 4 (*.f64 (PI.f64) f)) 3) 1/3))) (/.f64 -4 (PI.f64)))
	14.0b	(log.f64 (pow.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))))
	14.6b	(pow.f64 (cbrt.f64 (log.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))))) 3)
	2.1b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (*.f64 (PI.f64) f)))) -4)))

Compiler

Compiled 3282 to 2268 computations (30.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 4 (log1p.f64 (expm1.f64 (*.f64 (PI.f64) f))))
✓	0.4b	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (*.f64 (PI.f64) -1/4))
✓	1.0b	(log1p.f64 (expm1.f64 (*.f64 (PI.f64) f)))
	1.0b	(*.f64 (PI.f64) 1/12)

series26.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

8.0ms	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (*.f64 (PI.f64) -1/4))	f	-inf
5.0ms	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (*.f64 (PI.f64) -1/4))	f	inf
5.0ms	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (*.f64 (PI.f64) -1/4))	f	0
2.0ms	(/.f64 4 (log1p.f64 (expm1.f64 (*.f64 (PI.f64) f))))	f	0
2.0ms	(/.f64 4 (log1p.f64 (expm1.f64 (*.f64 (PI.f64) f))))	f	-inf

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

255×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
187×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	297	38
2	3637	38

Stop Event

1×	node limit

Counts

3 → 90

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
309×	`sub-neg_binary64`
300×	`unswap-sqr_binary64`
200×	`fma-def_binary64`
183×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	720
1	278	711
2	851	702
3	3041	693

Stop Event

1×	node limit

Counts

126 → 114

prune115.0ms (0.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	129	14	143

Error

1.3b

Counts

143 → 14

Alt Table

Status	Error	Program
	62.0b	(log1p.f64 (-.f64 (pow.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))) 1))
	2.1b	(-.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)))))
✓	2.0b	(/.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (*.f64 (PI.f64) -1/4))
	2.8b	(.f64 (/.f64 (sqrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (cbrt.f64 (.f64 (pow.f64 (PI.f64) 2) 1/16))) (/.f64 (sqrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (cbrt.f64 (*.f64 (PI.f64) -1/4))))
	2.3b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	2.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) 2) (cbrt.f64 (.f64 (pow.f64 (PI.f64) 2) 1/16))) (cbrt.f64 (.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (*.f64 (PI.f64) f)))) (/.f64 -4 (PI.f64)))))
	2.3b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f)))) 3) (pow.f64 (*.f64 (PI.f64) -1/4) 3)))
	2.3b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	61.3b	(.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))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) 1) (/.f64 -4 (PI.f64)))
	3.0b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) 2) (.f64 (cbrt.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	61.3b	(.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) 3)) (/.f64 -4 (PI.f64)))
	2.9b	(pow.f64 (cbrt.f64 (.f64 (log.f64 (fma.f64 (PI.f64) (.f64 1/12 f) (/.f64 4 (*.f64 (PI.f64) f)))) (/.f64 -4 (PI.f64)))) 3)
	47.3b	(.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (pow.f64 (pow.f64 (/.f64 4 (*.f64 (PI.f64) f)) 3) 1/3))) (/.f64 -4 (PI.f64)))
	2.1b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 (PI.f64) 1/12) f (/.f64 4 (*.f64 (PI.f64) f)))) -4)))

Compiler

Compiled 3271 to 2194 computations (32.9% saved)

regimes813.0ms (5.5%)

Accuracy

Total 0.6b remaining (27.9%)

Threshold costs 0.6b (27.9%)

Counts

134 → 1

Compiler

Compiled 18858 to 14264 computations (24.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	83
1	45	83

Stop Event

1×

saturated

end286.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 466 to 351 computations (24.7% saved)

Details

analyze1.4s (9.2%)

sample10.6s (72%)

preprocess30.0ms (0.2%)

simplify26.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series438.0ms (3%)

rewrite114.0ms (0.8%)

simplify51.0ms (0.3%)

prune245.0ms (1.7%)

localize10.0ms (0.1%)

series26.0ms (0.2%)

rewrite56.0ms (0.4%)

simplify33.0ms (0.2%)

prune108.0ms (0.7%)

localize10.0ms (0.1%)

series23.0ms (0.2%)

rewrite52.0ms (0.4%)

simplify36.0ms (0.2%)

prune134.0ms (0.9%)

localize11.0ms (0.1%)

series26.0ms (0.2%)

rewrite57.0ms (0.4%)

simplify36.0ms (0.2%)

prune115.0ms (0.8%)

regimes813.0ms (5.5%)

simplify3.0ms (0%)

end286.0ms (1.9%)

Profiling