Details

analyze2.0s (20.1%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample51.0ms (0.5%)

Algorithm

1×

intervals

Results

33.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	3.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	5.8b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	7.3b	(/.f64 (.f64 y t) (.f64 2 z))

rewrite92.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`add-sqr-sqrt_binary64`
118×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
81×	`times-frac_binary64`
78×	`prod-diff_binary64`

Counts

4 → 203

Calls

4 calls:

24.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
11.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
9.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
8.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series360.0ms (3.7%)

Counts

4 → 156

Calls

4 calls:

122.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
112.0ms	(/.f64 (.f64 y t) (.f64 2 z))
67.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
58.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

simplify543.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-neg_binary64`
273×	`exp-prod_binary64`
232×	`times-frac_binary64`
230×	`associate-/l*_binary64`
215×	`associate-*r/_binary64`

Counts

359 → 648

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	10640
1	1154	8682
2	3814	7711
3	4584	7711
4	4860	7711

prune478.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	645	3	648
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	647	3	650

Error

Counts

650 → 3

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	3.1b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))))))
	19.8b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 11336 to 5659 computations (50.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	0.0b	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))
✓	4.7b	(*.f64 (/.f64 y 2) (/.f64 t z))
✓	5.8b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

rewrite79.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
72×	`add-cube-cbrt_binary64`
68×	`times-frac_binary64`
48×	`prod-diff_binary64`

Counts

4 → 182

Calls

4 calls:

18.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
17.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
6.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
5.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

series483.0ms (4.9%)

Counts

4 → 156

Calls

4 calls:

202.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
148.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
72.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))
61.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify469.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

285×	`fma-neg_binary64`
275×	`distribute-neg-frac_binary64`
251×	`cancel-sign-sub-inv_binary64`
247×	`associate-*r/_binary64`
230×	`associate-*l/_binary64`

Counts

338 → 594

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	416	9325
1	1131	7563
2	3407	6952
3	4955	6942
4	4882	6942

prune472.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	594	0	594
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	594	3	597

Error

Counts

597 → 3

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	3.1b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))))))
	19.8b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 9312 to 4742 computations (49.1% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.3b	(/.f64 (.f64 y t) (.f64 2 z))
	17.6b	(cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))
	17.6b	(cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))
✓	17.6b	(cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`div-inv_binary64`

Counts

1 → 16

Calls

1 calls:

5.0ms

(cbrt.f64 (/.f64 (*.f64 y t) (*.f64 2 z)))

series2.2s (22.3%)

Counts

1 → 36

Calls

1 calls:

2.2s	(cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))

simplify155.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-neg_binary64`
733×	`div-sub_binary64`
717×	`fma-def_binary64`
509×	`exp-sum_binary64`
292×	`exp-diff_binary64`

Counts

52 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	1049
1	174	1049
2	282	965
3	799	797
4	1936	785
5	4110	785
6	4907	785
7	4947	785

prune293.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	479	0	479
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	479	3	482

Error

Counts

482 → 3

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	3.1b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))))))
▶	19.8b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 5826 to 3223 computations (44.7% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 2 (/.f64 z t) x)

series58.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

58.0ms

(fma.f64 2 (/.f64 z t) x)

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-*l/_binary64`
542×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
443×	`associate-+l+_binary64`
396×	`fma-def_binary64`

Counts

46 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	376
1	23	359
2	49	359
3	126	359
4	432	359
5	1628	359
6	4283	359
7	4686	359
8	4929	359
9	4999	359

prune16.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	74	3	77

Error

Counts

77 → 3

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	3.1b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))) (cbrt.f64 (/.f64 (.f64 y t) (.f64 2 z)))))))
✓	19.8b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 202 to 108 computations (46.5% saved)

regimes227.0ms (2.3%)

Accuracy

Total 1.0b remaining (99.4%)

Threshold costs 1.0b (99.4%)

Compiler

Compiled 1822 to 1222 computations (32.9% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	20	19
2	36	19
3	48	19
4	57	19
5	61	19
6	62	19
7	62	19

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample1.6s (16.3%)

Algorithm

1×

intervals

Results

962.0ms

8000×

body

128

valid

Compiler

Compiled 106 to 70 computations (34% saved)

Details

analyze2.0s (20.1%)

sample51.0ms (0.5%)

simplify73.0ms (0.7%)

prune8.0ms (0.1%)

localize20.0ms (0.2%)

rewrite92.0ms (0.9%)

series360.0ms (3.7%)

simplify543.0ms (5.5%)

prune478.0ms (4.8%)

localize18.0ms (0.2%)

rewrite79.0ms (0.8%)

series483.0ms (4.9%)

simplify469.0ms (4.8%)

prune472.0ms (4.8%)

localize26.0ms (0.3%)

rewrite7.0ms (0.1%)

series2.2s (22.3%)

simplify155.0ms (1.6%)

prune293.0ms (3%)

localize9.0ms (0.1%)

rewrite2.0ms (0%)

series58.0ms (0.6%)

simplify124.0ms (1.3%)

prune16.0ms (0.2%)

regimes227.0ms (2.3%)

simplify10.0ms (0.1%)

end1.0ms (0%)

sample1.6s (16.3%)

Profiling