Details

analyze780.0ms (17.9%)

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
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (25.7%)

Results

956.0ms	8256×	body	128	valid
68.0ms	647×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify111.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune1.0ms (0%)

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

2.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.8b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series50.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
19.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

9.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
8.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify120.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune112.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	6	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	7	194

Error

Counts

194 → 7

Alt Table

Status	Error	Program
▶	2.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	30.2b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	45.4b	(.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 z 3) (pow.f64 y 3))) (.f64 t (fma.f64 y (+.f64 y z) (*.f64 z z))))
	9.3b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	9.4b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	11.3b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.8b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 4618 to 1331 computations (71.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
✓	2.6b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

series76.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

30.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
27.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
19.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite79.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
335×	`add-sqr-sqrt_binary64`
323×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
98×	`associate-l_binary64`

Counts

3 → 332

Calls

3 calls:

19.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
11.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
7.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify206.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

543×	`sub-neg_binary64`
246×	`associate-/l*_binary64`
241×	`fma-neg_binary64`
211×	`+-commutative_binary64`
210×	`associate--l+_binary64`

Counts

452 → 498

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	10707
1	1107	10159
2	4250	9700
3	5224	9700

prune248.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	496	2	498
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	500	5	505

Error

Counts

505 → 5

Alt Table

Status	Error	Program
	7.5b	(.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y))) 1)) (*.f64 t (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z y)))))
	9.3b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
▶	2.6b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	11.3b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.8b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 12469 to 3990 computations (68% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	2.5b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

series31.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

31.0ms

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

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

1 → 144

Calls

1 calls:

9.0ms

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

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

925×	`times-frac_binary64`
628×	`fma-def_binary64`
239×	`associate-/r/_binary64`
193×	`associate-/l/_binary64`
168×	`associate-*l/_binary64`

Counts

192 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	5536
1	818	5389
2	3076	5259
3	4983	5259

prune131.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	305	5	310

Error

Counts

310 → 5

Alt Table

Status	Error	Program
▶	9.3b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	2.6b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	11.4b	(/.f64 1 (/.f64 (-.f64 z y) (*.f64 t (-.f64 x y))))
	11.3b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.8b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 7249 to 1678 computations (76.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z y))
✓	9.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))

series49.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

34.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
15.0ms	(/.f64 t (-.f64 z y))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 87

Calls

2 calls:

15.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
3.0ms	(/.f64 t (-.f64 z y))

simplify143.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
695×	`fma-def_binary64`
344×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`
204×	`sub-neg_binary64`

Counts

159 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3780
1	617	3669
2	2394	3214
3	4765	3214
4	4978	3214

prune74.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
✓	9.3b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	2.6b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	11.4b	(/.f64 1 (/.f64 (-.f64 z y) (*.f64 t (-.f64 x y))))
	11.3b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.8b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 3370 to 928 computations (72.5% saved)

regimes700.0ms (16.1%)

Accuracy

Total 1.9b remaining (99.3%)

Threshold costs 0b (0%)

Counts

72 → 3

Compiler

Compiled 8309 to 4662 computations (43.9% saved)

bsearch41.0ms (0.9%)

Steps

Iters	Range		Point
8	8.171317614974743e-215	1.360791217921543e-211	5.712395648754913e-212
8	-6.537309713167231e-107	-7.90525689562175e-110	-1.3228102918677774e-107

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`/-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	58
1	33	58
2	38	58
3	40	58
4	41	58
5	40	58

end66.0ms (1.5%)

Compiler: Compiled 151 to 82 computations (45.7% saved)

Details

analyze780.0ms (17.9%)

sample1.1s (25.7%)

simplify111.0ms (2.5%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series50.0ms (1.2%)

rewrite25.0ms (0.6%)

simplify120.0ms (2.7%)

prune112.0ms (2.6%)

localize8.0ms (0.2%)

series76.0ms (1.8%)

rewrite79.0ms (1.8%)

simplify206.0ms (4.7%)

prune248.0ms (5.7%)

localize6.0ms (0.1%)

series31.0ms (0.7%)

rewrite28.0ms (0.6%)

simplify116.0ms (2.7%)

prune131.0ms (3%)

localize6.0ms (0.1%)

series49.0ms (1.1%)

rewrite23.0ms (0.5%)

simplify143.0ms (3.3%)

prune74.0ms (1.7%)

regimes700.0ms (16.1%)

bsearch41.0ms (0.9%)

simplify4.0ms (0.1%)

end66.0ms (1.5%)

Profiling