Details

analyze962.0ms (18.1%)

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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify54.0ms (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

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

2.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.7b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	10.3b	(-.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 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	4.6b	(/.f64 (.f64 y t) (.f64 2 z))

series101.0ms (1.9%)

Counts

4 → 156

Calls

4 calls:

44.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
30.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
14.0ms	(/.f64 (.f64 y t) (.f64 2 z))
11.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite51.0ms (1%)

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

simplify273.0ms (5.1%)

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

prune257.0ms (4.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	305	4	309
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	307	4	311

Error

0.0b

Counts

311 → 4

Alt Table

Status	Error	Program
	23.9b	(fma.f64 2 (/.f64 z t) x)
	2.7b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
	3.0b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 z (.f64 1/2 (/.f64 (.f64 y t) z))))))
▶	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 11566 to 5786 computations (50% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series105.0ms (2%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(-.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))
13.0ms	(-.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 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
8.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
4.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
3.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

simplify216.0ms (4.1%)

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 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	416	9997
1	1131	7851
2	3407	6952
3	4955	6942
4	4882	6942

prune224.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	278	4	282

Error

0.0b

Counts

282 → 4

Alt Table

Status	Error	Program
	23.9b	(fma.f64 2 (/.f64 z t) x)
▶	2.7b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
	3.0b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 z (.f64 1/2 (/.f64 (.f64 y t) z))))))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 9568 to 4880 computations (49% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
✓	3.6b	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)
	4.6b	(/.f64 (.f64 y t) (.f64 2 z))

series93.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

45.0ms	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
30.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
18.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

rewrite124.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

546×	`times-frac_binary64`
438×	`add-sqr-sqrt_binary64`
429×	`*-un-lft-identity_binary64`
320×	`add-cube-cbrt_binary64`
186×	`prod-diff_binary64`

Counts

3 → 413

Calls

3 calls:

25.0ms	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
8.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
7.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

simplify485.0ms (9.1%)

Algorithm

1×	egg-herbie

Rules

368×	`cancel-sign-sub-inv_binary64`
253×	`fma-neg_binary64`
245×	`div-sub_binary64`
241×	`distribute-neg-frac_binary64`
188×	`*-commutative_binary64`

Counts

533 → 503

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	405	25783
1	1042	19853
2	3218	16279
3	4569	15775
4	4768	15775

prune552.0ms (10.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	537	2	539
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	539	4	543

Error

Counts

543 → 4

Alt Table

Status	Error	Program
	23.9b	(fma.f64 2 (/.f64 z t) x)
▶	0.1b	(-.f64 x (/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))))
	2.8b	(-.f64 x (/.f64 1 (.f64 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))) (/.f64 1 y))))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 27368 to 15528 computations (43.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (/.f64 t z))
✓	0.0b	(-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))
✓	0.0b	(-.f64 x (/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))))
✓	0.5b	(/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z))))

series94.0ms (1.8%)

Counts

4 → 84

Calls

4 calls:

43.0ms	(-.f64 x (/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))))
30.0ms	(/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z))))
14.0ms	(-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))
7.0ms	(*.f64 1/2 (/.f64 t z))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
75×	`times-frac_binary64`
61×	`prod-diff_binary64`

Counts

4 → 196

Calls

4 calls:

12.0ms	(-.f64 x (/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))))
6.0ms	(-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))
6.0ms	(/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z))))
5.0ms	(*.f64 1/2 (/.f64 t z))

simplify211.0ms (4%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
298×	`fma-neg_binary64`
187×	`cancel-sign-sub-inv_binary64`
129×	`*-commutative_binary64`
129×	`distribute-neg-frac_binary64`

Counts

280 → 289

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	342	9152
1	848	7543
2	2588	6414
3	4736	6404
4	4823	6404

prune245.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	289	4	293

Error

Counts

293 → 4

Alt Table

Status	Error	Program
	23.9b	(fma.f64 2 (/.f64 z t) x)
✓	0.1b	(-.f64 x (/.f64 1 (-.f64 (/.f64 z y) (*.f64 1/2 (/.f64 t z)))))
	2.8b	(-.f64 x (/.f64 1 (.f64 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))) (/.f64 1 y))))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 9870 to 5088 computations (48.4% saved)

regimes278.0ms (5.2%)

Accuracy

Total 0.1b remaining (94.2%)

Threshold costs 0.1b (94.2%)

Counts

48 → 1

Compiler

Compiled 5218 to 3556 computations (31.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	24	19
2	36	19
3	44	19
4	50	19
5	53	19
6	54	19
7	51	19

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample840.0ms (15.8%)

Algorithm

1×

intervals

Results

488.0ms

8000×

body

128

valid

Compiler

Compiled 108 to 76 computations (29.6% saved)

Details

analyze962.0ms (18.1%)

sample26.0ms (0.5%)

simplify54.0ms (1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series101.0ms (1.9%)

rewrite51.0ms (1%)

simplify273.0ms (5.1%)

prune257.0ms (4.8%)

localize9.0ms (0.2%)

series105.0ms (2%)

rewrite41.0ms (0.8%)

simplify216.0ms (4.1%)

prune224.0ms (4.2%)

localize10.0ms (0.2%)

series93.0ms (1.8%)

rewrite124.0ms (2.3%)

simplify485.0ms (9.1%)

prune552.0ms (10.4%)

localize9.0ms (0.2%)

series94.0ms (1.8%)

rewrite47.0ms (0.9%)

simplify211.0ms (4%)

prune245.0ms (4.6%)

regimes278.0ms (5.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample840.0ms (15.8%)

Profiling