Details

analyze3.7s (24.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample4.5s (29.4%)

Results

2.7s	8256×	body	128	valid
1.7s	5143×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
433×	`exp-sum_binary64`
321×	`distribute-rgt-in_binary64`
303×	`distribute-lft-in_binary64`
279×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	136	40
3	512	40
4	2106	40
5	4520	40
6	4992	40

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

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.3b	(/.f64 2/3 t)
✓	2.3b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	8.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series137.0ms (0.9%)

Counts

4 → 88

Calls

4 calls:

64.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
41.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
30.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2/3 t)

rewrite82.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`prod-diff_binary64`
202×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
189×	`add-log-exp_binary64`

Counts

4 → 87

Calls

4 calls:

76.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
76.0ms	(/.f64 2/3 t)
76.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
76.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	53
1	394	53
2	4874	53
3	5989	53
0	0	0
1	0	0

simplify156.0ms (1%)

Algorithm

1×	egg-herbie

Rules

590×	`associate--r+_binary64`
467×	`associate-r_binary64`
435×	`associate-l_binary64`
416×	`cancel-sign-sub-inv_binary64`
254×	`fma-def_binary64`

Counts

175 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2727
1	604	2679
2	2021	2658
3	4821	2656
4	4984	2656
5	4964	2656

prune320.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	3	161

Error

0.0b

Counts

161 → 3

Alt Table

Status	Error	Program
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
▶	16.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 5875 to 3110 computations (47.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
✓	0.0b	(+.f64 a 5/6)
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
✓	0.1b	(*.f64 (+.f64 a 5/6) (-.f64 c b))

series670.0ms (4.4%)

Counts

4 → 144

Calls

4 calls:

619.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
34.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
15.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))
2.0ms	(+.f64 a 5/6)

rewrite114.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

513×	`prod-diff_binary64`
168×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
157×	`add-log-exp_binary64`

Counts

4 → 122

Calls

4 calls:

108.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
108.0ms	(+.f64 a 5/6)
108.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
108.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	328	51
2	4180	51
3	5140	51
0	0	0
1	0	0

simplify263.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
488×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
333×	`*-commutative_binary64`
218×	`associate-r_binary64`

Counts

266 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	635	9164
1	2225	8966
2	5126	8966

prune578.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	204	3	207

Error

Counts

207 → 3

Alt Table

Status	Error	Program
▶	16.7b	(/.f64 x (fma.f64 y (log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))))) x))
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 12559 to 8121 computations (35.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))))
	0.0b	(+.f64 a 5/6)
	0.0b	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
	0.1b	(*.f64 (+.f64 a 5/6) (-.f64 c b))

series29.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

29.0ms

(log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))))

rewrite95.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

431×	`prod-diff_binary64`
277×	`fma-def_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
144×	`fma-neg_binary64`

Counts

1 → 35

Calls

1 calls:

93.0ms

(log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	259	15
2	3212	15
3	4928	15
0	0	0
1	0	0

simplify137.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

373×	`cancel-sign-sub-inv_binary64`
367×	`associate--l+_binary64`
303×	`associate-r_binary64`
244×	`distribute-rgt-out_binary64`
216×	`associate-l_binary64`

Counts

71 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1590
1	550	1549
2	2199	1289
3	4657	1289
4	4980	1289
5	5051	1289

prune394.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	190	3	193

Error

Counts

193 → 3

Alt Table

Status	Error	Program
✓	16.7b	(/.f64 x (fma.f64 y (log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))))) x))
▶	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 6688 to 4289 computations (35.9% saved)

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 t))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
	0.3b	(/.f64 2/3 t)
✓	1.8b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

series135.0ms (0.9%)

Counts

3 → 51

Calls

3 calls:

99.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))
28.0ms	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
8.0ms	(sqrt.f64 (/.f64 1 t))

rewrite92.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

334×	`log1p-udef_binary64`
188×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
175×	`add-cbrt-cube_binary64`

Counts

3 → 68

Calls

3 calls:

89.0ms	(sqrt.f64 (/.f64 1 t))
89.0ms	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
89.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	377	32
2	4779	32
3	5200	32
0	0	0
1	0	0

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

501×	`associate--l+_binary64`
415×	`associate-+l-_binary64`
386×	`distribute-lft-out--_binary64`
357×	`+-commutative_binary64`
351×	`fma-neg_binary64`

Counts

119 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	1720
1	183	1681
2	575	1510
3	1566	1396
4	3506	1171
5	4262	1171
6	5146	1171

prune200.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	110	3	113

Error

Counts

113 → 3

Alt Table

Status	Error	Program
✓	16.7b	(/.f64 x (fma.f64 y (log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))))) x))
✓	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 3063 to 1811 computations (40.9% saved)

regimes3.1s (20.5%)

Accuracy

Total 0.9b remaining (88.4%)

Threshold costs 0.9b (88.4%)

Counts

110 → 3

Compiler

Compiled 36506 to 27183 computations (25.5% saved)

bsearch81.0ms (0.5%)

Steps

Iters	Range		Point
4	3.4073320166746997e-282	8.276599410265367e-275	5.914976321355086e-279
1	-1.8216588890627468e-73	-1.1596361154539363e-80	-4.598639463012585e-77

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	119
1	66	119
2	80	119
3	88	119
4	93	119
5	94	119
6	92	119

end199.0ms (1.3%)

Compiler: Compiled 257 to 172 computations (33.1% saved)

Details

analyze3.7s (24.1%)

sample4.5s (29.4%)

simplify48.0ms (0.3%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series137.0ms (0.9%)

rewrite82.0ms (0.5%)

simplify156.0ms (1%)

prune320.0ms (2.1%)

localize24.0ms (0.2%)

series670.0ms (4.4%)

rewrite114.0ms (0.7%)

simplify263.0ms (1.7%)

prune578.0ms (3.8%)

localize28.0ms (0.2%)

series29.0ms (0.2%)

rewrite95.0ms (0.6%)

simplify137.0ms (0.9%)

prune394.0ms (2.6%)

localize41.0ms (0.3%)

series135.0ms (0.9%)

rewrite92.0ms (0.6%)

simplify138.0ms (0.9%)

prune200.0ms (1.3%)

regimes3.1s (20.5%)

bsearch81.0ms (0.5%)

simplify10.0ms (0.1%)

end199.0ms (1.3%)

Profiling