Details

analyze1.5s (24.1%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.3s (21.3%)

Results

1.1s	8255×	body	128	valid
64.0ms	495×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify102.0ms (1.7%)

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 (0.1%)

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

2.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	2.5b	(-.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 (-.f64 t z) 1)
✓	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series51.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

48.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
4.0ms	(+.f64 (-.f64 t z) 1)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
13×	`associate-+l+_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

2 → 45

Calls

2 calls:

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

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

574×	`cancel-sign-sub-inv_binary64`
349×	`times-frac_binary64`
307×	`sub-neg_binary64`
236×	`fma-neg_binary64`
214×	`+-commutative_binary64`

Counts

129 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	3461
1	774	3300
2	3474	3231
3	4999	3231

prune103.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Error

0.0b

Counts

122 → 5

Alt Table

Status	Error	Program
✓	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	34.2b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
▶	7.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
	30.8b	(fma.f64 (/.f64 a (fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)) (-.f64 z y) x)
	33.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)))

Compiler

Compiled 3606 to 1642 computations (54.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
✓	0.0b	(-.f64 (+.f64 1 t) z)
✓	2.5b	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
✓	6.4b	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

series90.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
28.0ms	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))
23.0ms	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
4.0ms	(-.f64 (+.f64 1 t) z)

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 125

Calls

4 calls:

20.0ms	(-.f64 (+.f64 1 t) z)
9.0ms	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
6.0ms	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
6.0ms	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
428×	`associate-/l*_binary64`
314×	`associate-/r*_binary64`
276×	`fma-neg_binary64`
220×	`associate-r_binary64`

Counts

221 → 271

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	453	5782
1	1282	5352
2	4890	5352
3	5104	5352

prune333.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	317	1	318
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	318	5	323

Error

Counts

323 → 5

Alt Table

Status	Error	Program
▶	7.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (.f64 (*.f64 y a) (/.f64 1 (-.f64 (+.f64 1 t) z))))
	33.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)))
✓	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	34.2b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	30.8b	(fma.f64 (/.f64 a (fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)) (-.f64 z y) x)

Compiler

Compiled 11435 to 5732 computations (49.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (+.f64 1 t) z)
✓	0.0b	(/.f64 1 (-.f64 (+.f64 1 t) z))
✓	2.6b	(.f64 (.f64 y a) (/.f64 1 (-.f64 (+.f64 1 t) z)))
	6.4b	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

series45.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

35.0ms	(.f64 (.f64 y a) (/.f64 1 (-.f64 (+.f64 1 t) z)))
9.0ms	(/.f64 1 (-.f64 (+.f64 1 t) z))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64`

Counts

2 → 98

Calls

2 calls:

11.0ms	(.f64 (.f64 y a) (/.f64 1 (-.f64 (+.f64 1 t) z)))
6.0ms	(/.f64 1 (-.f64 (+.f64 1 t) z))

simplify105.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

403×	`cancel-sign-sub-inv_binary64`
350×	`times-frac_binary64`
292×	`associate-+r+_binary64`
250×	`associate-/l*_binary64`
238×	`+-commutative_binary64`

Counts

170 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	4172
1	976	3957
2	3950	3949
3	5011	3949

prune314.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	340	5	345

Error

Counts

345 → 5

Alt Table

Status	Error	Program
✓	7.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (.f64 (*.f64 y a) (/.f64 1 (-.f64 (+.f64 1 t) z))))
	33.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)))
✓	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	34.2b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
▶	30.8b	(fma.f64 (/.f64 a (fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)) (-.f64 z y) x)

Compiler

Compiled 12588 to 6856 computations (45.5% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)
✓	1.3b	(fma.f64 (/.f64 a (fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)) (-.f64 z y) x)

series357.0ms (5.9%)

Counts

2 → 52

Calls

2 calls:

298.0ms	(fma.f64 (/.f64 a (fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)) (-.f64 z y) x)
59.0ms	(fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

617×	`times-frac_binary64`
551×	`fma-def_binary64`
517×	`associate-/l*_binary64`
359×	`fma-neg_binary64`
279×	`associate-/r*_binary64`

Counts

72 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	2160
1	356	1963
2	1290	1424
3	4786	1424
4	5039	1424

prune51.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	71	5	76

Error

Counts

76 → 5

Alt Table

Status	Error	Program
✓	7.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (.f64 (*.f64 y a) (/.f64 1 (-.f64 (+.f64 1 t) z))))
	33.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)))
✓	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	34.2b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	30.8b	(fma.f64 (/.f64 a (fma.f64 (sqrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 t z)) 1)) (-.f64 z y) x)

Compiler

Compiled 2011 to 983 computations (51.1% saved)

regimes1.2s (19.5%)

Accuracy

Total 0.4b remaining (97.8%)

Threshold costs 0.4b (97.8%)

Counts

91 → 3

Compiler

Compiled 14170 to 9466 computations (33.2% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
7	1.4982704715914885e-29	1.829120351847473e-27	4.65178715222157e-28
9	-1.0809116173157452e+117	-4.789827571933521e+107	-4.878938494260088e+107

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	75
1	39	75
2	52	75
3	65	75
4	73	75
5	76	75
6	77	75
7	76	75

end96.0ms (1.6%)

Compiler: Compiled 235 to 139 computations (40.9% saved)

Details

analyze1.5s (24.1%)

sample1.3s (21.3%)

simplify102.0ms (1.7%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series51.0ms (0.9%)

rewrite8.0ms (0.1%)

simplify79.0ms (1.3%)

prune103.0ms (1.7%)

localize11.0ms (0.2%)

series90.0ms (1.5%)

rewrite47.0ms (0.8%)

simplify130.0ms (2.2%)

prune333.0ms (5.5%)

localize13.0ms (0.2%)

series45.0ms (0.7%)

rewrite25.0ms (0.4%)

simplify105.0ms (1.7%)

prune314.0ms (5.2%)

localize13.0ms (0.2%)

series357.0ms (5.9%)

rewrite1.0ms (0%)

simplify74.0ms (1.2%)

prune51.0ms (0.9%)

regimes1.2s (19.5%)

bsearch42.0ms (0.7%)

simplify4.0ms (0.1%)

end96.0ms (1.6%)

Profiling