Details

analyze637.0ms (12%)

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)

sample103.0ms (1.9%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	19×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify117.0ms (2.2%)

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

1.9b

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)

localize7.0ms (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)

series53.0ms (1%)

Counts

2 → 84

Calls

2 calls:

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

simplify121.0ms (2.3%)

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

prune165.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

Counts

194 → 9

Alt Table

Status	Error	Program
▶	1.2b	(.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 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	47.3b	(.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 z 3) (pow.f64 y 3))) (.f64 (+.f64 (.f64 z z) (+.f64 (.f64 y y) (*.f64 z y))) t))
	13.4b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	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)
	3.0b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
	32.5b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	11.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	9.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 4787 to 1401 computations (70.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
✓	0.5b	(cbrt.f64 (-.f64 z y))
✓	0.5b	(cbrt.f64 (-.f64 x y))

series129.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
36.0ms	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
29.0ms	(cbrt.f64 (-.f64 z y))
28.0ms	(cbrt.f64 (-.f64 x y))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
58×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
28×	`cbrt-div_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 150

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
2.0ms	(cbrt.f64 (-.f64 x y))
2.0ms	(cbrt.f64 (-.f64 z y))

simplify131.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

420×	`associate-r_binary64`
395×	`times-frac_binary64`
371×	`fma-neg_binary64`
315×	`associate-l_binary64`
230×	`fma-def_binary64`

Counts

246 → 289

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	425	6024
1	1123	5824
2	3769	5644
3	4975	5644

prune332.0ms (6.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	491	9	500

Error

Counts

500 → 9

Alt Table

Status	Error	Program
✓	1.2b	(.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 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	47.3b	(.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 z 3) (pow.f64 y 3))) (.f64 (+.f64 (.f64 z z) (+.f64 (.f64 y y) (*.f64 z y))) t))
	13.4b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	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)
	3.0b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
	32.5b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	11.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	9.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 22862 to 7006 computations (69.4% saved)

localize7.0ms (0.1%)

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)

series72.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

31.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
20.0ms	(/.f64 (-.f64 z y) (-.f64 x y))
20.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))

rewrite82.0ms (1.5%)

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:

17.0ms	(*.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))

simplify261.0ms (4.9%)

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

prune303.0ms (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	495	3	498
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	500	7	507

Error

Counts

507 → 7

Alt Table

Status	Error	Program
	15.9b	(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) t)
	13.4b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	3.0b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
▶	1.7b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	11.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	1.9b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 (-.f64 x y) (-.f64 z y)))) t)

Compiler

Compiled 12567 to 4028 computations (67.9% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	1.6b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

series34.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

33.0ms

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

rewrite31.0ms (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:

12.0ms

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

simplify121.0ms (2.3%)

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

prune158.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	303	2	305
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	305	7	312

Error

Counts

312 → 7

Alt Table

Status	Error	Program
	1.8b	(/.f64 1 (/.f64 (/.f64 (-.f64 z y) (-.f64 x y)) t))
	13.4b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
✓	1.7b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	11.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	1.9b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 (-.f64 x y) (-.f64 z y)))) t)
	18.4b	(/.f64 t (cbrt.f64 (pow.f64 (/.f64 (-.f64 z y) (-.f64 x y)) 3)))

Compiler

Compiled 7243 to 1677 computations (76.8% saved)

regimes1.2s (22.5%)

Accuracy

Total 1.0b remaining (98.5%)

Threshold costs 0b (0%)

Counts

171 → 1

Compiler

Compiled 24702 to 13993 computations (43.4% 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)

sample1.2s (22%)

Algorithm

1×

intervals

Results

787.0ms	8000×	body	128	valid
27.0ms	639×	body	128	invalid

Compiler

Compiled 155 to 94 computations (39.4% saved)

Details

analyze637.0ms (12%)

sample103.0ms (1.9%)

simplify117.0ms (2.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series53.0ms (1%)

rewrite25.0ms (0.5%)

simplify121.0ms (2.3%)

prune165.0ms (3.1%)

localize12.0ms (0.2%)

series129.0ms (2.4%)

rewrite32.0ms (0.6%)

simplify131.0ms (2.5%)

prune332.0ms (6.2%)

localize7.0ms (0.1%)

series72.0ms (1.4%)

rewrite82.0ms (1.5%)

simplify261.0ms (4.9%)

prune303.0ms (5.7%)

localize9.0ms (0.2%)

series34.0ms (0.6%)

rewrite31.0ms (0.6%)

simplify121.0ms (2.3%)

prune158.0ms (3%)

regimes1.2s (22.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (22%)

Profiling