Details

analyze1.8s (34.3%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.2s (22.9%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

simplify57.0ms (1.1%)

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

prune17.0ms (0.3%)

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

2.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.1b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	11.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	3.8b	(/.f64 (.f64 y t) (.f64 2 z))
✓	5.1b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

series125.0ms (2.4%)

Counts

4 → 156

Calls

4 calls:

67.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
31.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
14.0ms	(/.f64 (.f64 y t) (.f64 2 z))
13.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite50.0ms (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:

11.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
6.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
5.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify245.0ms (4.6%)

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 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	11732
1	1154	9150
2	3814	7711
3	4584	7711
4	4860	7711

prune259.0ms (4.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	309	3	312
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	311	3	314

Error

Counts

314 → 3

Alt Table

Status	Error	Program
	22.7b	(fma.f64 2 (/.f64 z t) x)
▶	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	3.3b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)))

Compiler

Compiled 11557 to 5775 computations (50% saved)

localize10.0ms (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)))
✓	5.1b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
✓	5.5b	(*.f64 (/.f64 y 2) (/.f64 t z))

series113.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

53.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
31.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
16.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
14.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

rewrite41.0ms (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:

9.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
8.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
3.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
3.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

simplify221.0ms (4.2%)

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 → 277

Iterations

Useful iterations: 3 (0.0ms)

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

prune218.0ms (4.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	277	3	280

Error

Counts

280 → 3

Alt Table

Status	Error	Program
	22.7b	(fma.f64 2 (/.f64 z t) x)
✓	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	3.3b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)))

Compiler

Compiled 9507 to 4846 computations (49% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))
✓	0.7b	(/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y))
✓	5.0b	(/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)
✓	7.0b	(*.f64 (/.f64 y z) t)

series78.0ms (1.5%)

Counts

4 → 144

Calls

4 calls:

31.0ms	(/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y))
19.0ms	(/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)
14.0ms	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))
13.0ms	(*.f64 (/.f64 y z) t)

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`times-frac_binary64`
69×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 164

Calls

4 calls:

6.0ms	(/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y))
5.0ms	(*.f64 (/.f64 y z) t)
4.0ms	(/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)
4.0ms	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))

simplify174.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

414×	`fma-def_binary64`
408×	`associate-/r/_binary64`
355×	`associate-/l/_binary64`
176×	`distribute-rgt-neg-in_binary64`
151×	`distribute-lft-neg-in_binary64`

Counts

308 → 280

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	6364
1	609	5930
2	2160	5310
3	4859	5310
4	4886	5310

prune204.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	280	3	283

Error

Counts

283 → 3

Alt Table

Status	Error	Program
▶	22.7b	(fma.f64 2 (/.f64 z t) x)
✓	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	3.3b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)))

Compiler

Compiled 7081 to 3426 computations (51.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

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

rewrite1.0ms (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:

0.0ms

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

simplify81.0ms (1.5%)

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 → 14

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

prune8.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	14	3	17

Error

Counts

17 → 3

Alt Table

Status	Error	Program
✓	22.7b	(fma.f64 2 (/.f64 z t) x)
✓	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	3.3b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))) y)))

Compiler

Compiled 185 to 99 computations (46.5% saved)

regimes235.0ms (4.4%)

Accuracy

Total 0.1b remaining (92.1%)

Threshold costs 0.1b (92.1%)

Counts

33 → 1

Compiler

Compiled 3982 to 2632 computations (33.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	17	17
2	23	17
3	25	17
4	26	17
5	23	17

end54.0ms (1%)

Compiler: Compiled 78 to 53 computations (32.1% saved)

Details

analyze1.8s (34.3%)

sample1.2s (22.9%)

simplify57.0ms (1.1%)

prune17.0ms (0.3%)

localize9.0ms (0.2%)

series125.0ms (2.4%)

rewrite50.0ms (0.9%)

simplify245.0ms (4.6%)

prune259.0ms (4.9%)

localize10.0ms (0.2%)

series113.0ms (2.1%)

rewrite41.0ms (0.8%)

simplify221.0ms (4.2%)

prune218.0ms (4.1%)

localize11.0ms (0.2%)

series78.0ms (1.5%)

rewrite32.0ms (0.6%)

simplify174.0ms (3.3%)

prune204.0ms (3.9%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify81.0ms (1.5%)

prune8.0ms (0.2%)

regimes235.0ms (4.4%)

simplify3.0ms (0.1%)

end54.0ms (1%)

Profiling