Details

analyze1.2s (18.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.3s (21.1%)

Results

981.0ms	8256×	body	128	valid
307.0ms	2626×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
245×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	107	13
4	326	11
5	814	11
6	1834	11
7	3225	11
8	3920	11
9	3976	11
10	4006	11
11	4011	11
12	4011	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	6.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	4.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series30.0ms (0.5%)

Counts

2 → 88

Calls

2 calls:

22.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
9.0ms	(/.f64 (-.f64 t z) a)

rewrite98.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
214×	`fma-def_binary64`
192×	`egg-rr`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	197	18
2	2825	18

Stop Event

1×	node limit

Counts

2 → 192

Calls

2 calls:

92.0ms	(/.f64 (-.f64 t z) a)
92.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1054×	`fma-def_binary64`
632×	`fma-neg_binary64`
167×	`cancel-sign-sub-inv_binary64`
157×	`distribute-rgt-in_binary64`
157×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	944
1	74	944
2	164	908
3	391	774
4	823	774
5	1625	774
6	2748	774
7	3535	774
8	3756	774
9	3813	774
10	3813	774

Stop Event

1×

saturated

Counts

280 → 214

prune148.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	211	5	216

Error

0.0b

Counts

216 → 5

Alt Table

Status	Error	Program
	6.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	4.8b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (-.f64 t z) a)) 3) x)
	4.5b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
▶	3.3b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
	12.8b	(fma.f64 y (+.f64 (fma.f64 t (/.f64 1 a) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a)) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (.f64 a a)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a))) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (.f64 a a))) (.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a)) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (*.f64 a a)))))) x)

Compiler

Compiled 7201 to 2038 computations (71.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.1b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

series21.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

21.0ms

(fma.f64 (-.f64 t z) (/.f64 y a) x)

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
446×	`prod-diff_binary64`
200×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	194	11
2	2692	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

44.0ms

(fma.f64 (-.f64 t z) (/.f64 y a) x)

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
669×	`fma-neg_binary64`
185×	`cancel-sign-sub-inv_binary64`
109×	`distribute-rgt-in_binary64`
103×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	694
1	61	694
2	134	680
3	323	590
4	674	590
5	1143	590
6	1986	590
7	3107	590
8	3483	590
9	3525	590
10	3555	590
11	3560	590
12	3560	590

Stop Event

1×

saturated

Counts

89 → 46

prune30.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	44	7	51

Error

Counts

51 → 7

Alt Table

Status	Error	Program
	6.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	4.8b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (-.f64 t z) a)) 3) x)
	4.5b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
▶	4.4b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2))
✓	3.3b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
	12.8b	(fma.f64 y (+.f64 (fma.f64 t (/.f64 1 a) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a)) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (.f64 a a)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a))) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (.f64 a a))) (.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a)) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (*.f64 a a)))))) x)
	35.5b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)

Compiler

Compiled 876 to 301 computations (65.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x))
	3.1b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

series472.0ms (7.4%)

Counts

3 → 180

Calls

3 calls:

243.0ms

(pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)

184.0ms

(cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x))

44.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2))

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
123×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	276	40
2	3317	40

Stop Event

1×	node limit

Counts

3 → 60

Calls

3 calls:

53.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2))

53.0ms

(pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)

53.0ms

(cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x))

simplify197.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
402×	`*-commutative_binary64`
193×	`sub-neg_binary64`
188×	`+-commutative_binary64`
151×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	966	15572
1	3705	15300

Stop Event

1×	node limit

Counts

240 → 270

prune560.0ms (8.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	481	7	488

Error

Counts

488 → 7

Alt Table

Status	Error	Program
	6.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	4.8b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (-.f64 t z) a)) 3) x)
▶	4.5b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
✓	4.4b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2))
✓	3.3b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
	12.8b	(fma.f64 y (+.f64 (fma.f64 t (/.f64 1 a) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a)) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (.f64 a a)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a))) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (.f64 a a))) (.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 a)) (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (*.f64 a a)))))) x)
	35.5b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)

Compiler

Compiled 31711 to 14417 computations (54.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 a (-.f64 t z)) -1)
✓	4.2b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)

series147.0ms (2.3%)

Counts

2 → 96

Calls

2 calls:

83.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
64.0ms	(pow.f64 (/.f64 a (-.f64 t z)) -1)

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

441×	`prod-diff_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
204×	`fma-def_binary64`
122×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	236	18
2	3151	18

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

53.0ms	(pow.f64 (/.f64 a (-.f64 t z)) -1)
53.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary64`
706×	`fma-neg_binary64`
184×	`cancel-sign-sub-inv_binary64`
109×	`distribute-rgt-in_binary64`
99×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	922
1	68	922
2	141	830
3	334	830
4	713	830
5	1187	830
6	2042	830
7	2983	830
8	3600	830
9	3640	830
10	3645	830
11	3645	830

Stop Event

1×

saturated

Counts

165 → 89

prune65.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	90	6	96

Error

Counts

96 → 6

Alt Table

Status	Error	Program
✓	4.4b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2))
	6.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	3.3b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
	4.9b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a)) x)
	4.5b	(fma.f64 y (*.f64 (/.f64 1 a) (-.f64 t z)) x)
	35.5b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)

Compiler

Compiled 1222 to 387 computations (68.3% saved)

regimes1.4s (22.5%)

Accuracy

Total 0.9b remaining (97.1%)

Threshold costs 0.9b (97.1%)

Counts

72 → 3

Compiler

Compiled 11932 to 7430 computations (37.7% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`
8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	65
1	35	65
2	47	65
3	61	65
4	73	65
5	91	65
6	104	65
7	110	65
8	116	65
9	117	65

Stop Event

1×

saturated

end85.0ms (1.3%)

Compiler: Compiled 203 to 106 computations (47.8% saved)

Details

analyze1.2s (18.9%)

sample1.3s (21.1%)

simplify50.0ms (0.8%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series30.0ms (0.5%)

rewrite98.0ms (1.5%)

simplify84.0ms (1.3%)

prune148.0ms (2.3%)

localize6.0ms (0.1%)

series21.0ms (0.3%)

rewrite45.0ms (0.7%)

simplify80.0ms (1.3%)

prune30.0ms (0.5%)

localize10.0ms (0.2%)

series472.0ms (7.4%)

rewrite54.0ms (0.9%)

simplify197.0ms (3.1%)

prune560.0ms (8.8%)

localize7.0ms (0.1%)

series147.0ms (2.3%)

rewrite54.0ms (0.9%)

simplify125.0ms (2%)

prune65.0ms (1%)

regimes1.4s (22.5%)

bsearch2.0ms (0%)

simplify8.0ms (0.1%)

end85.0ms (1.3%)

Profiling