Details

analyze1.3s (13.5%)

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
0.4%	99.4%	0.2%	10
5.6%	94.2%	0.2%	11
7.1%	92.7%	0.2%	12
8.8%	91%	0.2%	13
15.6%	84.2%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample73.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 42 to 30 computations (28.6% saved)

simplify101.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
683×	`sub-neg_binary64`
438×	`neg-mul-1_binary64`
412×	`neg-sub0_binary64`
378×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	66	19
3	158	17
4	344	17
5	846	17
6	2066	17
7	3773	17
8	4182	17
9	4701	17
10	4906	17
11	4923	17

prune4.0ms (0%)

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

1.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	2.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 63 computations (37% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series74.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

49.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
24.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
8×	`distribute-lft-out_binary64`

Counts

2 → 49

Calls

2 calls:

5.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify138.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

379×	`times-frac_binary64`
371×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
277×	`+-commutative_binary64`
256×	`associate-/l*_binary64`

Counts

145 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	349	4823
1	1015	4738
2	4256	4723
3	4982	4723
4	5014	4723

prune124.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	143	5	148

Error

0.0b

Counts

148 → 5

Alt Table

Status	Error	Program
	39.6b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 a (-.f64 (+.f64 1 t) z)) (-.f64 z y) x) 3))
✓	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	37.2b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	9.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
▶	2.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 4622 to 2253 computations (51.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	9.4b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series132.0ms (1.4%)

Counts

3 → 144

Calls

3 calls:

70.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
52.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
10.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite187.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

1052×	`*-un-lft-identity_binary64`
883×	`times-frac_binary64`
649×	`add-sqr-sqrt_binary64`
448×	`add-cube-cbrt_binary64`
300×	`prod-diff_binary64`

Counts

3 → 600

Calls

3 calls:

38.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
16.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
6.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify852.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

435×	`times-frac_binary64`
336×	`sub-neg_binary64`
248×	`fma-def_binary64`
208×	`fma-udef_binary64`
196×	`neg-sub0_binary64`

Counts

744 → 670

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1050	52563
1	3195	48069
2	4814	47566
3	4994	47566

prune629.0ms (6.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	668	2	670
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	671	4	675

Error

Counts

675 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	2.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	7.9b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a))))
▶	0.4b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

Compiler

Compiled 34644 to 14868 computations (57.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	0.0b	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
✓	1.1b	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

series158.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

67.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
59.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
31.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 126

Calls

3 calls:

14.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
11.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
3.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

simplify197.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
374×	`associate-/l*_binary64`
277×	`associate-/r*_binary64`
246×	`+-commutative_binary64`
207×	`sub-neg_binary64`

Counts

270 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	658	10133
1	1956	9941
2	4965	9941
3	4992	9941

prune259.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	292	4	296

Error

Counts

296 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	2.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	7.9b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a))))
✓	0.4b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

Compiler

Compiled 10895 to 5195 computations (52.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	10.1b	(/.f64 (/.f64 (-.f64 y z) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))

series213.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

73.0ms	(/.f64 (/.f64 (-.f64 y z) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))
66.0ms	(/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
38.0ms	(cbrt.f64 a)
36.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))

rewrite542.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Rules

4343×	`times-frac_binary64`
3062×	`*-un-lft-identity_binary64`
1840×	`add-sqr-sqrt_binary64`
1342×	`add-cube-cbrt_binary64`
634×	`cbrt-prod_binary64`

Counts

4 → 1565

Calls

4 calls:

42.0ms	(/.f64 (/.f64 (-.f64 y z) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))
4.0ms	(/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
4.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify1.6s (17.5%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-/r/_binary64`
576×	`associate-/l/_binary64`
565×	`times-frac_binary64`
513×	`div-sub_binary64`
108×	`associate-/l*_binary64`

Counts

1649 → 1279

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1129	86617
1	3291	84601
2	5599	84601

prune1.1s (11.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	1311	0	1311
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	1311	4	1315

Error

Counts

1315 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	2.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	7.9b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a))))
✓	0.4b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

Compiler

Compiled 57966 to 24262 computations (58.1% saved)

regimes751.0ms (8.1%)

Accuracy

Total 0.3b remaining (96.2%)

Threshold costs 0.3b (96.2%)

Counts

98 → 1

Compiler

Compiled 15010 to 9963 computations (33.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	19
2	40	19
3	54	19
4	73	19
5	81	19
6	82	19
7	78	19

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample805.0ms (8.7%)

Algorithm

1×

intervals

Results

388.0ms	8000×	body	128	valid
22.0ms	503×	body	128	invalid

Compiler

Compiled 122 to 82 computations (32.8% saved)

Details

analyze1.3s (13.5%)

sample73.0ms (0.8%)

simplify101.0ms (1.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series74.0ms (0.8%)

rewrite8.0ms (0.1%)

simplify138.0ms (1.5%)

prune124.0ms (1.3%)

localize8.0ms (0.1%)

series132.0ms (1.4%)

rewrite187.0ms (2%)

simplify852.0ms (9.2%)

prune629.0ms (6.8%)

localize9.0ms (0.1%)

series158.0ms (1.7%)

rewrite37.0ms (0.4%)

simplify197.0ms (2.1%)

prune259.0ms (2.8%)

localize15.0ms (0.2%)

series213.0ms (2.3%)

rewrite542.0ms (5.8%)

simplify1.6s (17.5%)

prune1.1s (11.8%)

regimes751.0ms (8.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample805.0ms (8.7%)

Profiling