Details

analyze733.0ms (15.6%)

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)

sample1.0s (22.2%)

Results

881.0ms	8256×	body	128	valid
67.0ms	654×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify110.0ms (2.3%)

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

prune2.0ms (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

1.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.8b	(*.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))
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series47.0ms (1%)

Counts

2 → 84

Calls

2 calls:

29.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
18.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite25.0ms (0.5%)

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)
6.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify124.0ms (2.6%)

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

prune136.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
	48.8b	(.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (.f64 (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))) t))
	11.6b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	22.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	2.4b	(.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y)))) t)
	25.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (sqrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
▶	1.9b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

Compiler

Compiled 4679 to 1345 computations (71.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
✓	1.7b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)

series55.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

30.0ms	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
18.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
7.0ms	(/.f64 1 (-.f64 z y))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`
24×	`associate-r_binary64`

Counts

3 → 125

Calls

3 calls:

10.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
10.0ms	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
5.0ms	(/.f64 1 (-.f64 z y))

simplify105.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
441×	`cancel-sign-sub-inv_binary64`
364×	`sub-neg_binary64`
202×	`associate-l_binary64`
191×	`fma-neg_binary64`

Counts

233 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	5123
1	791	4796
2	2905	4505
3	5071	4505

prune196.0ms (4.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	244	8	252

Error

0.0b

Counts

252 → 8

Alt Table

Status	Error	Program
	48.8b	(.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (.f64 (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))) t))
	11.6b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	22.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	2.4b	(.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y)))) t)
✓	1.9b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
▶	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	32.2b	(/.f64 (.f64 t (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (-.f64 z y))) (+.f64 x y))
	36.1b	(/.f64 (.f64 t (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 x y) (-.f64 z y)))

Compiler

Compiled 5639 to 2188 computations (61.2% 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)))
✓	1.7b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

series70.0ms (1.5%)

Counts

3 → 120

Calls

3 calls:

31.0ms	(*.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))

rewrite81.0ms (1.7%)

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:

22.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
9.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
7.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify214.0ms (4.6%)

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

prune293.0ms (6.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	496	2	498
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	498	8	506

Error

Counts

506 → 8

Alt Table

Status	Error	Program
	48.8b	(.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (.f64 (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))) t))
	11.6b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	22.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	1.9b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
✓	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	32.6b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (-.f64 z y)) (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))))) (/.f64 t (/.f64 (sqrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 x y)))))
	32.2b	(/.f64 (.f64 t (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (-.f64 z y))) (+.f64 x y))
▶	1.8b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

Compiler

Compiled 12602 to 4058 computations (67.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	1.8b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

series30.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

30.0ms

(/.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 (2.5%)

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

prune165.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	302	3	305
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	306	7	313

Error

Counts

313 → 7

Alt Table

Status	Error	Program
	9.5b	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))
	32.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (sqrt.f64 (-.f64 z y))) (/.f64 t (/.f64 (sqrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 x y)))))
	1.8b	(/.f64 t (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y))))
✓	1.9b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
✓	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	11.6b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	32.2b	(/.f64 (.f64 t (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (-.f64 z y))) (+.f64 x y))

Compiler

Compiled 7265 to 1680 computations (76.9% saved)

regimes971.0ms (20.7%)

Accuracy

Total 1.0b remaining (98.8%)

Threshold costs 0b (0%)

Counts

173 → 1

Compiler

Compiled 20342 to 11702 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

end85.0ms (1.8%)

Compiler: Compiled 194 to 98 computations (49.5% saved)

Details

analyze733.0ms (15.6%)

sample1.0s (22.2%)

simplify110.0ms (2.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series47.0ms (1%)

rewrite25.0ms (0.5%)

simplify124.0ms (2.6%)

prune136.0ms (2.9%)

localize7.0ms (0.2%)

series55.0ms (1.2%)

rewrite33.0ms (0.7%)

simplify105.0ms (2.2%)

prune196.0ms (4.2%)

localize7.0ms (0.2%)

series70.0ms (1.5%)

rewrite81.0ms (1.7%)

simplify214.0ms (4.6%)

prune293.0ms (6.3%)

localize7.0ms (0.1%)

series30.0ms (0.6%)

rewrite28.0ms (0.6%)

simplify116.0ms (2.5%)

prune165.0ms (3.5%)

regimes971.0ms (20.7%)

simplify3.0ms (0.1%)

end85.0ms (1.8%)

Profiling