Details

analyze676.0ms (15.3%)

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
3.1%	96.7%	0.2%	8
19.9%	79.9%	0.2%	9
22.8%	77%	0.2%	10
35.1%	64.7%	0.2%	11
45%	54.8%	0.2%	12
53.8%	45.1%	1.2%	13
56.2%	42.4%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample99.0ms (2.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% 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

1.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.9b	(*.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))
✓	1.8b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series54.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
22.0ms	(/.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:

10.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
6.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify125.0ms (2.8%)

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

prune131.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	186	8	194

Error

Counts

194 → 8

Alt Table

Status	Error	Program
	11.2b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	41.7b	(.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 (-.f64 z y) (fma.f64 y (+.f64 y x) (*.f64 x x)))) t)
	2.0b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
▶	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	17.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
	2.9b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	1.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	8.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))

Compiler

Compiled 4642 to 1353 computations (70.9% saved)

localize7.0ms (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)))
✓	1.8b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

series71.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

32.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
20.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
19.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite80.0ms (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:

20.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
11.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
6.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify220.0ms (5%)

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

prune291.0ms (6.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	496	2	498
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	500	6	506

Error

Counts

506 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	17.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
	2.9b	(.f64 (.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	1.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	8.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
▶	1.5b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

Compiler

Compiled 12501 to 4012 computations (67.9% 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))
✓	1.5b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

series32.0ms (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:

10.0ms

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

simplify118.0ms (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

prune152.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	305	6	311

Error

Counts

311 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	17.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
▶	2.9b	(.f64 (.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	1.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	8.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.5b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

Compiler

Compiled 7307 to 1710 computations (76.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	1.8b	(.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series288.0ms (6.5%)

Counts

4 → 120

Calls

4 calls:

177.0ms	(.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
45.0ms	(.f64 (.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
36.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
30.0ms	(cbrt.f64 t)

rewrite80.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
142×	`*-un-lft-identity_binary64`
112×	`add-exp-log_binary64`
105×	`associate-l_binary64`

Counts

4 → 235

Calls

4 calls:

21.0ms	(.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
18.0ms	(.f64 (.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
6.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify168.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-r_binary64`
480×	`associate-l_binary64`
401×	`fma-neg_binary64`
265×	`associate-/l*_binary64`
156×	`times-frac_binary64`

Counts

355 → 397

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	401	8594
1	1097	7103
2	4717	7103
3	5077	7103

prune215.0ms (4.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	431	0	431
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	431	6	437

Error

Counts

437 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	17.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
✓	2.9b	(.f64 (.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	1.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	8.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.5b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

Compiler

Compiled 12402 to 4114 computations (66.8% saved)

regimes718.0ms (16.3%)

Accuracy

Total 1.0b remaining (98.7%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 12847 to 7382 computations (42.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	20	49
2	26	49
3	28	49
4	29	49
5	29	49

end1.0ms (0%)

Compiler: Compiled 35 to 14 computations (60% saved)

sample692.0ms (15.7%)

Algorithm

1×

intervals

Results

315.0ms	8000×	body	128	valid
25.0ms	595×	body	128	invalid

Compiler

Compiled 149 to 85 computations (43% saved)

Details

analyze676.0ms (15.3%)

sample99.0ms (2.3%)

simplify111.0ms (2.5%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series54.0ms (1.2%)

rewrite25.0ms (0.6%)

simplify125.0ms (2.8%)

prune131.0ms (3%)

localize7.0ms (0.2%)

series71.0ms (1.6%)

rewrite80.0ms (1.8%)

simplify220.0ms (5%)

prune291.0ms (6.6%)

localize6.0ms (0.1%)

series32.0ms (0.7%)

rewrite28.0ms (0.6%)

simplify118.0ms (2.7%)

prune152.0ms (3.5%)

localize12.0ms (0.3%)

series288.0ms (6.5%)

rewrite80.0ms (1.8%)

simplify168.0ms (3.8%)

prune215.0ms (4.9%)

regimes718.0ms (16.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample692.0ms (15.7%)

Profiling