Details

analyze516.0ms (18.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
9.4%	90.5%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
37.8%	60.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
56.8%	36.2%	7%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample926.0ms (33.6%)

Results

765.0ms	8256×	body	128	valid
72.0ms	803×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify114.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1119×	`div-sub_binary64`
816×	`fma-def_binary64`
804×	`fma-neg_binary64`
517×	`neg-mul-1_binary64`
483×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	27	10
3	57	10
4	111	10
5	180	10
6	312	10
7	977	10
8	3166	10
9	3725	10
10	4150	10
11	4786	10
12	4803	10
13	4958	10
14	5387	10

Stop Event

1×	node limit

Counts

1 → 1

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.4b	(/.f64 (*.f64 x (-.f64 y z)) y)

series13.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(/.f64 (*.f64 x (-.f64 y z)) y)

rewrite44.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`log1p-expm1-u_binary64`
918×	`expm1-log1p-u_binary64`
386×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
77×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	157	10
2	2262	10
3	6391	10

Stop Event

1×	node limit

Counts

1 → 43

Calls

1 calls:

43.0ms

(/.f64 (*.f64 x (-.f64 y z)) y)

simplify105.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1005×	`fma-neg_binary64`
595×	`neg-sub0_binary64`
564×	`neg-mul-1_binary64`
424×	`distribute-neg-frac_binary64`
394×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	330
1	24	330
2	55	330
3	101	330
4	188	330
5	327	330
6	764	330
7	2667	330
8	3566	330
9	4068	330
10	4901	330
11	4844	330
12	4874	330

Stop Event

1×	node limit

Counts

79 → 48

prune32.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Error

0.0b

Counts

49 → 7

Alt Table

Status	Error	Program
▶	4.7b	(*.f64 x (/.f64 1 (/.f64 y (-.f64 y z))))
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
	38.2b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) y)) 2)
	9.5b	(*.f64 (/.f64 x y) (-.f64 y z))
	38.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 y)))
	11.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 y z))) 2) (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 y)))
	4.7b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 y)))

Compiler

Compiled 744 to 271 computations (63.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 y z))
✓	0.1b	(/.f64 1 (/.f64 y (-.f64 y z)))
✓	4.3b	(*.f64 x (/.f64 1 (/.f64 y (-.f64 y z))))

series26.0ms (1%)

Counts

3 → 84

Calls

3 calls:

15.0ms	(*.f64 x (/.f64 1 (/.f64 y (-.f64 y z))))
7.0ms	(/.f64 y (-.f64 y z))
5.0ms	(/.f64 1 (/.f64 y (-.f64 y z)))

rewrite88.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
386×	`prod-diff_binary64`
188×	`fma-def_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	199	24
2	2621	24
3	5410	24

Stop Event

1×	node limit

Counts

3 → 115

Calls

3 calls:

86.0ms	(/.f64 y (-.f64 y z))
86.0ms	(/.f64 1 (/.f64 y (-.f64 y z)))
86.0ms	(*.f64 x (/.f64 1 (/.f64 y (-.f64 y z))))

simplify84.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-neg_binary64`
494×	`fma-def_binary64`
493×	`associate-/l*_binary64`
428×	`associate-/r*_binary64`
415×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	939
1	116	939
2	330	849
3	1227	819
4	4528	819
5	4956	819
6	4986	819
7	4968	819

Stop Event

1×	node limit

Counts

199 → 137

prune120.0ms (4.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Error

Counts

144 → 7

Alt Table

Status	Error	Program
✓	4.7b	(*.f64 x (/.f64 1 (/.f64 y (-.f64 y z))))
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
	38.2b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) y)) 2)
	9.5b	(*.f64 (/.f64 x y) (-.f64 y z))
▶	4.6b	(*.f64 x (-.f64 1 (/.f64 z y)))
	38.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 y)))
	11.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 y z))) 2) (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 y)))

Compiler

Compiled 1986 to 831 computations (58.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.3b	(*.f64 x (-.f64 1 (/.f64 z y)))

series11.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

11.0ms

(*.f64 x (-.f64 1 (/.f64 z y)))

rewrite40.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

837×	`log1p-expm1-u_binary64`
837×	`expm1-log1p-u_binary64`
343×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
78×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	167	10
2	2119	10
3	5834	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

40.0ms

(*.f64 x (-.f64 1 (/.f64 z y)))

simplify38.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

376×	`fma-def_binary64`
181×	`fma-neg_binary64`
55×	`cancel-sign-sub-inv_binary64`
44×	`associate-r_binary64`
44×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	330
1	26	330
2	54	330
3	85	330
4	190	330
5	312	330
6	417	330
7	511	330
8	543	330
9	568	330
10	574	330
11	579	330
12	522	330

Stop Event

1×

saturated

Counts

57 → 26

prune37.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	26	7	33

Error

Counts

33 → 7

Alt Table

Status	Error	Program
✓	4.7b	(*.f64 x (/.f64 1 (/.f64 y (-.f64 y z))))
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
	38.2b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) y)) 2)
▶	9.5b	(*.f64 (/.f64 x y) (-.f64 y z))
✓	4.6b	(*.f64 x (-.f64 1 (/.f64 z y)))
	38.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 y)))
	11.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 y z))) 2) (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 y)))

Compiler

Compiled 434 to 246 computations (43.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.3b	(*.f64 (/.f64 x y) (-.f64 y z))

series14.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(*.f64 (/.f64 x y) (-.f64 y z))

rewrite46.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

912×	`log1p-expm1-u_binary64`
912×	`expm1-log1p-u_binary64`
377×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
77×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	157	10
2	2242	10
3	6320	10

Stop Event

1×	node limit

Counts

1 → 43

Calls

1 calls:

45.0ms

(*.f64 (/.f64 x y) (-.f64 y z))

simplify104.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1005×	`fma-neg_binary64`
595×	`neg-sub0_binary64`
564×	`neg-mul-1_binary64`
424×	`distribute-neg-frac_binary64`
394×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	330
1	24	330
2	55	330
3	101	330
4	188	330
5	327	330
6	764	330
7	2667	330
8	3566	330
9	4068	330
10	4901	330
11	4844	330
12	4874	330

Stop Event

1×	node limit

Counts

79 → 48

prune27.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	2	1	3
Picked	0	1	1
Done	1	2	3
Total	49	6	55

Error

Counts

55 → 6

Alt Table

Status	Error	Program
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
	38.8b	(/.f64 (/.f64 (*.f64 x (-.f64 y z)) (sqrt.f64 y)) (sqrt.f64 y))
	38.2b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) y)) 2)
✓	9.5b	(*.f64 (/.f64 x y) (-.f64 y z))
✓	4.6b	(*.f64 x (-.f64 1 (/.f64 z y)))
	9.8b	(/.f64 (-.f64 y z) (/.f64 y x))

Compiler

Compiled 657 to 228 computations (65.3% saved)

regimes195.0ms (7.1%)

Accuracy

Total 3.0b remaining (99.7%)

Threshold costs 0b (0%)

Counts

24 → 5

Compiler

Compiled 1223 to 753 computations (38.4% saved)

bsearch75.0ms (2.7%)

Steps

Iters	Range		Point
6	6.658662274313302e-73	9.608613872642728e-72	2.601515186109111e-72
10	1.6345289368248465e-235	3.464784157324588e-223	5.454120664480108e-224
8	-1.341117571525812e-165	-4.7783487479983356e-170	-3.3040369895347108e-167
6	-1.5721061290523406e+131	-1.3608831830736938e+128	-1.4989920815534833e+128

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	74
1	39	74
2	52	74
3	65	74
4	72	74
5	75	74
6	76	74
7	75	74

Stop Event

1×

saturated

end72.0ms (2.6%)

Compiler: Compiled 175 to 96 computations (45.1% saved)

Iter	Nodes	Cost
0	13	330
1	26	330
2	54	330
3	85	330
4	190	330
5	312	330
6	417	330
7	511	330
8	543	330
9	568	330
10	574	330
11	579	330
12	522	330

Iter	Nodes	Cost
0	13	330
1	26	330
2	54	330
3	85	330
4	190	330
5	312	330
6	417	330
7	511	330
8	543	330
9	568	330
10	574	330
11	579	330
12	522	330

Details

analyze516.0ms (18.7%)

sample926.0ms (33.6%)

simplify114.0ms (4.1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series13.0ms (0.5%)

rewrite44.0ms (1.6%)

simplify105.0ms (3.8%)

prune32.0ms (1.1%)

localize6.0ms (0.2%)

series26.0ms (1%)

rewrite88.0ms (3.2%)

simplify84.0ms (3.1%)

prune120.0ms (4.4%)

localize5.0ms (0.2%)

series11.0ms (0.4%)

rewrite40.0ms (1.5%)

simplify38.0ms (1.4%)

prune37.0ms (1.3%)

localize4.0ms (0.2%)

series14.0ms (0.5%)

rewrite46.0ms (1.7%)

simplify104.0ms (3.8%)

prune27.0ms (1%)

regimes195.0ms (7.1%)

bsearch75.0ms (2.7%)

simplify6.0ms (0.2%)

end72.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	13	330
1	26	330
2	54	330
3	85	330
4	190	330
5	312	330
6	417	330
7	511	330
8	543	330
9	568	330
10	574	330
11	579	330
12	522	330