Details

analyze1.2s (27%)

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
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.2s (26.1%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify55.0ms (1.2%)

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

prune4.0ms (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

1.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	10.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	1.9b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (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)))))
✓	5.5b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	5.7b	(/.f64 (.f64 y t) (.f64 2 z))

series108.0ms (2.4%)

Counts

4 → 156

Calls

4 calls:

46.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
32.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
17.0ms	(/.f64 (.f64 y t) (.f64 2 z))
13.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite54.0ms (1.2%)

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 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(/.f64 (.f64 y t) (.f64 2 z))
4.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

simplify258.0ms (5.7%)

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 → 309

Iterations

Useful iterations: 2 (0.0ms)

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

prune233.0ms (5.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	306	3	309
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	308	3	311

Error

Counts

311 → 3

Alt Table

Status	Error	Program
	1.9b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	21.8b	(fma.f64 2 (/.f64 z t) x)
▶	0.3b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))

Compiler

Compiled 11520 to 5760 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 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
✓	0.0b	(+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))
✓	4.3b	(*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))
✓	5.5b	(/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))))

series102.0ms (2.2%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
30.0ms	(/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))))
16.0ms	(*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))
12.0ms	(+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))

rewrite55.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
81×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
74×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

4 → 191

Calls

4 calls:

10.0ms	(*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))
8.0ms	(+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))
8.0ms	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
3.0ms	(/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))))

simplify276.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

297×	`fma-neg_binary64`
246×	`associate-*r/_binary64`
229×	`*-commutative_binary64`
217×	`associate-*l/_binary64`
183×	`associate-/l*_binary64`

Counts

347 → 324

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	10613
1	1194	8050
2	3633	7194
3	4655	7194
4	5000	7194
5	4817	7194

prune263.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	324	3	327

Error

Counts

327 → 3

Alt Table

Status	Error	Program
▶	1.9b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	21.8b	(fma.f64 2 (/.f64 z t) x)
✓	0.3b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))

Compiler

Compiled 11123 to 5998 computations (46.1% 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)))
✓	0.6b	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	5.1b	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
	5.7b	(/.f64 (.f64 y t) (.f64 2 z))

series67.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

33.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
33.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 89

Calls

2 calls:

11.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
6.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

simplify100.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-/r*_binary64`
520×	`associate-*l/_binary64`
347×	`fma-def_binary64`
216×	`associate-/r/_binary64`
174×	`associate-/l/_binary64`

Counts

161 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	4402
1	458	4169
2	1716	4122
3	5191	4122

prune177.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	248	3	251

Error

Counts

251 → 3

Alt Table

Status	Error	Program
✓	1.9b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
▶	21.8b	(fma.f64 2 (/.f64 z t) x)
✓	0.3b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))

Compiler

Compiled 6752 to 3782 computations (44% 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)

simplify82.0ms (1.8%)

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

prune10.0ms (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
✓	1.9b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	21.8b	(fma.f64 2 (/.f64 z t) x)
✓	0.3b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))

Compiler

Compiled 186 to 100 computations (46.2% saved)

regimes167.0ms (3.7%)

Accuracy

Total 1.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

28 → 1

Compiler

Compiled 2860 to 1930 computations (32.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	25	19
2	39	19
3	51	19
4	58	19
5	61	19
6	62	19
7	62	19

end54.0ms (1.2%)

Compiler: Compiled 81 to 54 computations (33.3% saved)

Details

analyze1.2s (27%)

sample1.2s (26.1%)

simplify55.0ms (1.2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series108.0ms (2.4%)

rewrite54.0ms (1.2%)

simplify258.0ms (5.7%)

prune233.0ms (5.1%)

localize10.0ms (0.2%)

series102.0ms (2.2%)

rewrite55.0ms (1.2%)

simplify276.0ms (6.1%)

prune263.0ms (5.8%)

localize9.0ms (0.2%)

series67.0ms (1.5%)

rewrite25.0ms (0.6%)

simplify100.0ms (2.2%)

prune177.0ms (3.9%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify82.0ms (1.8%)

prune10.0ms (0.2%)

regimes167.0ms (3.7%)

simplify3.0ms (0.1%)

end54.0ms (1.2%)

Profiling