Details

analyze1.6s (22.1%)

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)

sample1.2s (16.7%)

Results

1.1s	8256×	body	128	valid
60.0ms	492×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify94.0ms (1.3%)

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

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	1.5b	(-.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 a (+.f64 (-.f64 t z) 1))
✓	0.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series76.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

52.0ms	(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:

6.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify127.0ms (1.8%)

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

prune140.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	142	6	148

Error

Counts

148 → 6

Alt Table

Status	Error	Program
	39.3b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 a (-.f64 (+.f64 1 t) z)) (-.f64 z y) x) 3))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
	34.5b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
▶	1.0b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
	35.2b	(*.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)))
	1.5b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 4707 to 2304 computations (51.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 (-.f64 t z) 1))
✓	0.1b	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
✓	0.9b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)

series114.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

78.0ms	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
24.0ms	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
12.0ms	(/.f64 1 (+.f64 (-.f64 t z) 1))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 99

Calls

3 calls:

10.0ms	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
5.0ms	(/.f64 1 (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

441×	`times-frac_binary64`
429×	`associate-+r+_binary64`
385×	`associate-/l*_binary64`
311×	`associate-+l+_binary64`
249×	`associate-/r*_binary64`

Counts

219 → 232

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	443	6295
1	1284	6110
2	5448	6110

prune218.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	232	6	238

Error

Counts

238 → 6

Alt Table

Status	Error	Program
	34.5b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	1.0b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
	35.2b	(*.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)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
▶	1.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z))) (-.f64 z y) x)
	1.5b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 7068 to 3741 computations (47.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z)))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	0.9b	(fma.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z))) (-.f64 z y) x)

series170.0ms (2.4%)

Counts

4 → 120

Calls

4 calls:

63.0ms	(fma.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z))) (-.f64 z y) x)
36.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
36.0ms	(cbrt.f64 a)
35.0ms	(.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
48×	`associate-r_binary64`
38×	`times-frac_binary64`
38×	`cbrt-prod_binary64`

Counts

4 → 132

Calls

4 calls:

16.0ms	(.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z)))
4.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)
0.0ms	(fma.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z))) (-.f64 z y) x)

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-/l*_binary64`
429×	`times-frac_binary64`
410×	`associate-l_binary64`
281×	`associate-r_binary64`
242×	`associate-+l+_binary64`

Counts

252 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	434	6256
1	1242	5803
2	5299	5803

prune223.0ms (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	286	6	292

Error

Counts

292 → 6

Alt Table

Status	Error	Program
	34.5b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	1.0b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
	35.2b	(*.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)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z))) (-.f64 z y) x)
▶	1.5b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 8717 to 3873 computations (55.6% saved)

localize9.0ms (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)
✓	10.2b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series124.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

64.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
50.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
10.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite185.0ms (2.6%)

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:

36.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
12.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
6.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify789.0ms (11.2%)

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

prune641.0ms (9.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	669	1	670
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	670	6	676

Error

Counts

676 → 6

Alt Table

Status	Error	Program
	0.3b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	1.5b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	1.0b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
	35.2b	(*.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)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (-.f64 (+.f64 1 t) z))) (-.f64 z y) x)

Compiler

Compiled 34656 to 14873 computations (57.1% saved)

regimes1.0s (14.4%)

Accuracy

Total 0.3b remaining (97.2%)

Threshold costs 0.3b (97.2%)

Counts

141 → 1

Compiler

Compiled 21205 to 13911 computations (34.4% 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

end86.0ms (1.2%)

Compiler: Compiled 173 to 110 computations (36.4% saved)

Details

analyze1.6s (22.1%)

sample1.2s (16.7%)

simplify94.0ms (1.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series76.0ms (1.1%)

rewrite8.0ms (0.1%)

simplify127.0ms (1.8%)

prune140.0ms (2%)

localize9.0ms (0.1%)

series114.0ms (1.6%)

rewrite23.0ms (0.3%)

simplify95.0ms (1.3%)

prune218.0ms (3.1%)

localize12.0ms (0.2%)

series170.0ms (2.4%)

rewrite31.0ms (0.4%)

simplify101.0ms (1.4%)

prune223.0ms (3.2%)

localize9.0ms (0.1%)

series124.0ms (1.8%)

rewrite185.0ms (2.6%)

simplify789.0ms (11.2%)

prune641.0ms (9.1%)

regimes1.0s (14.4%)

simplify3.0ms (0%)

end86.0ms (1.2%)

Profiling