Details

analyze789.0ms (18.6%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	19×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify121.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1630×	`fma-neg_binary64`
896×	`div-sub_binary64`
582×	`times-frac_binary64`
579×	`fma-def_binary64`
367×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	74	13
4	145	13
5	245	13
6	572	13
7	1407	13
8	2937	13
9	2993	13
10	3292	13
11	3338	13
12	3355	13
13	3404	13
14	4948	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

10.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.6b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	10.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series40.0ms (1%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
9.0ms	(*.f64 x (-.f64 y z))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 81

Calls

2 calls:

8.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
5.0ms	(*.f64 x (-.f64 y z))

simplify108.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

526×	`cancel-sign-sub-inv_binary64`
513×	`fma-neg_binary64`
365×	`div-sub_binary64`
202×	`associate-/l*_binary64`
196×	`sub-neg_binary64`

Counts

165 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	2954
1	576	2753
2	2576	2555
3	4147	2552
4	5042	2552

prune100.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	6	146

Error

0.0b

Counts

146 → 6

Alt Table

Status	Error	Program
	1.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	36.8b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) (-.f64 t z))
	10.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	10.8b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))
▶	1.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	7.6b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (-.f64 y z) (cbrt.f64 (-.f64 t z))))

Compiler

Compiled 3241 to 964 computations (70.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	1.5b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

series63.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
25.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

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

simplify108.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
511×	`cancel-sign-sub-inv_binary64`
372×	`sub-neg_binary64`
220×	`fma-neg_binary64`
164×	`associate-/l*_binary64`

Counts

190 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4489
1	786	4288
2	2972	4076
3	5031	4076

prune108.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	179	8	187

Error

Counts

187 → 8

Alt Table

Status	Error	Program
	30.2b	(.f64 (.f64 x (/.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
▶	1.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	16.6b	(*.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 y z) (-.f64 t z)) 3)))
	36.8b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) (-.f64 t z))
	10.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	10.8b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))
✓	1.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	22.7b	(.f64 (.f64 x (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))))

Compiler

Compiled 4311 to 1294 computations (70% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series52.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

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

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 198

Calls

2 calls:

9.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
6.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

simplify165.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

562×	`cancel-sign-sub-inv_binary64`
374×	`sub-neg_binary64`
271×	`associate-/r/_binary64`
224×	`fma-neg_binary64`
198×	`associate-/l/_binary64`

Counts

282 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	7629
1	1057	7410
2	3983	7368
3	5298	7368

prune161.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	302	6	308

Error

Counts

308 → 6

Alt Table

Status	Error	Program
▶	9.4b	(/.f64 (/.f64 x (-.f64 t z)) (/.f64 1 (-.f64 y z)))
	10.8b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))
✓	1.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	36.8b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) (-.f64 t z))
	10.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
✓	1.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 7204 to 1689 computations (76.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	9.3b	(/.f64 (/.f64 x (-.f64 t z)) (/.f64 1 (-.f64 y z)))

series111.0ms (2.6%)

Counts

3 → 96

Calls

3 calls:

86.0ms	(/.f64 (/.f64 x (-.f64 t z)) (/.f64 1 (-.f64 y z)))
16.0ms	(/.f64 x (-.f64 t z))
9.0ms	(/.f64 1 (-.f64 y z))

rewrite136.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

1131×	`times-frac_binary64`
699×	`*-un-lft-identity_binary64`
699×	`add-sqr-sqrt_binary64`
419×	`add-cube-cbrt_binary64`
140×	`distribute-lft-out--_binary64`

Counts

3 → 591

Calls

3 calls:

19.0ms	(/.f64 (/.f64 x (-.f64 t z)) (/.f64 1 (-.f64 y z)))
4.0ms	(/.f64 1 (-.f64 y z))
4.0ms	(/.f64 x (-.f64 t z))

simplify437.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
566×	`associate-/l/_binary64`
323×	`associate-/r/_binary64`
315×	`associate-*l/_binary64`
308×	`associate-/r*_binary64`

Counts

687 → 671

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	560	21169
1	1509	19981
2	4897	19780
3	5545	19780

prune316.0ms (7.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	671	0	671
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	671	6	677

Error

Counts

677 → 6

Alt Table

Status	Error	Program
✓	9.4b	(/.f64 (/.f64 x (-.f64 t z)) (/.f64 1 (-.f64 y z)))
	10.8b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))
✓	1.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	36.8b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) (-.f64 t z))
	10.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
✓	1.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 18269 to 5631 computations (69.2% saved)

regimes539.0ms (12.7%)

Accuracy

Total 1.5b remaining (99%)

Threshold costs 0b (0%)

Counts

88 → 3

Compiler

Compiled 7470 to 4469 computations (40.2% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	73
1	35	73
2	45	73
3	56	73
4	62	73
5	65	73
6	66	73
7	66	73

end1.0ms (0%)

Compiler: Compiled 53 to 22 computations (58.5% saved)

sample737.0ms (17.4%)

Algorithm

1×

intervals

Results

325.0ms	8000×	body	128	valid
24.0ms	640×	body	128	invalid

Compiler

Compiled 159 to 91 computations (42.8% saved)

Details

analyze789.0ms (18.6%)

sample24.0ms (0.6%)

simplify121.0ms (2.9%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series40.0ms (1%)

rewrite19.0ms (0.4%)

simplify108.0ms (2.5%)

prune100.0ms (2.4%)

localize6.0ms (0.1%)

series63.0ms (1.5%)

rewrite28.0ms (0.7%)

simplify108.0ms (2.5%)

prune108.0ms (2.5%)

localize6.0ms (0.1%)

series52.0ms (1.2%)

rewrite40.0ms (0.9%)

simplify165.0ms (3.9%)

prune161.0ms (3.8%)

localize9.0ms (0.2%)

series111.0ms (2.6%)

rewrite136.0ms (3.2%)

simplify437.0ms (10.3%)

prune316.0ms (7.4%)

regimes539.0ms (12.7%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample737.0ms (17.4%)

Profiling