Details

analyze1.0s (13.1%)

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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.2s (15.6%)

Results

1.1s	8256×	body	128	valid
41.0ms	335×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify94.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

8.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	10.4b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series143.0ms (1.8%)

Counts

4 → 114

Calls

4 calls:

83.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
48.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)
5.0ms	(-.f64 (*.f64 t z) x)

rewrite68.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
10×	`distribute-lft-out_binary64`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
9.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 y z) x)
3.0ms	(-.f64 (*.f64 t z) x)

simplify188.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
544×	`fma-neg_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
201×	`associate--l+_binary64`

Counts

231 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	8297
1	1260	7857
2	4933	7855
3	5379	7855

prune335.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	256	7	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	257	7	264

Error

0.0b

Counts

264 → 7

Alt Table

Status	Error	Program
	25.2b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
	29.1b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
▶	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	8.5b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	16.7b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	45.5b	(/.f64 (+.f64 x (-.f64 (fma.f64 (/.f64 y (pow.f64 t 3)) (.f64 (/.f64 x z) (/.f64 x z)) (fma.f64 (/.f64 y (pow.f64 t 4)) (/.f64 (pow.f64 x 3) (pow.f64 z 3)) (fma.f64 (/.f64 y (.f64 t t)) (/.f64 x z) (/.f64 y t)))) (+.f64 (+.f64 (/.f64 x (.f64 t z)) (.f64 (/.f64 x (.f64 t z)) (/.f64 x (.f64 t z)))) (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 t z) 3))))) (+.f64 x 1))

Compiler

Compiled 9701 to 3650 computations (62.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x 1))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	2.7b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.3b	(/.f64 z (-.f64 (*.f64 t z) x))

series178.0ms (2.3%)

Counts

4 → 144

Calls

4 calls:

125.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
23.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
20.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
9.0ms	(/.f64 y (+.f64 x 1))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`

Counts

4 → 107

Calls

4 calls:

5.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 y (+.f64 x 1))
0.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify151.0ms (2%)

Algorithm

1×	egg-herbie

Rules

408×	`times-frac_binary64`
329×	`associate-/l*_binary64`
276×	`fma-neg_binary64`
255×	`associate-/r*_binary64`
250×	`+-commutative_binary64`

Counts

251 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7626
1	1119	7175
2	4600	7050
3	4982	7050

prune371.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	262	8	270

Error

0.0b

Counts

270 → 8

Alt Table

Status	Error	Program
▶	1.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (cbrt.f64 z) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	8.5b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	25.2b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
	10.7b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 z (-.f64 (.f64 z t) x)) 3)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
✓	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	8.1b	(+.f64 (/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	16.7b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))

Compiler

Compiled 10580 to 4076 computations (61.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 z)
	2.7b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	4.2b	(/.f64 (cbrt.f64 z) (-.f64 (*.f64 z t) x))
✓	4.2b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (cbrt.f64 z) (-.f64 (*.f64 z t) x)))

series127.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

65.0ms	(/.f64 (cbrt.f64 z) (-.f64 (*.f64 z t) x))
33.0ms	(cbrt.f64 z)
29.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (cbrt.f64 z) (-.f64 (*.f64 z t) x)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
25×	`cbrt-prod_binary64`

Counts

3 → 105

Calls

3 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (cbrt.f64 z) (-.f64 (*.f64 z t) x)))
5.0ms	(/.f64 (cbrt.f64 z) (-.f64 (*.f64 z t) x))
1.0ms	(cbrt.f64 z)

simplify142.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-def_binary64`
406×	`associate-/l/_binary64`
305×	`unswap-sqr_binary64`
268×	`associate-l_binary64`
253×	`fma-neg_binary64`

Counts

189 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	4699
1	667	4340
2	2605	4222
3	4917	4221
4	5018	4221

prune392.0ms (5.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	297	8	305

Error

0.0b

Counts

305 → 8

Alt Table

Status	Error	Program
✓	1.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (cbrt.f64 z) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	8.5b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	25.2b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
	10.7b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 z (-.f64 (.f64 z t) x)) 3)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
✓	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	8.1b	(+.f64 (/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	16.7b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))

Compiler

Compiled 13113 to 4143 computations (68.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))
	2.7b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	12.9b	(/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (*.f64 z t) x)))

series172.0ms (2.2%)

Counts

2 → 84

Calls

2 calls:

156.0ms	(/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (*.f64 z t) x)))
15.0ms	(.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`associate-/r/_binary64`

Counts

2 → 74

Calls

2 calls:

8.0ms	(/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (*.f64 z t) x)))
7.0ms	(.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))

simplify127.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

848×	`times-frac_binary64`
503×	`associate-/r*_binary64`
460×	`associate-/l*_binary64`
218×	`fma-def_binary64`
133×	`distribute-rgt-in_binary64`

Counts

158 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	6299
1	1235	5455
2	4866	5450
3	4986	5450

prune390.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	270	2	272
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	274	6	280

Error

0.0b

Counts

280 → 6

Alt Table

Status	Error	Program
✓	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	14.7b	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (.f64 z t) x))) 3)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	25.2b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
	8.5b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	4.3b	(+.f64 (/.f64 z (/.f64 (+.f64 1 x) (/.f64 y (-.f64 (.f64 z t) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 11871 to 4680 computations (60.6% saved)

regimes2.3s (30.1%)

Accuracy

Total 0.7b remaining (97%)

Threshold costs 0.7b (97%)

Counts

280 → 2

Compiler

Compiled 40609 to 24068 computations (40.7% saved)

bsearch13.0ms (0.2%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	121
1	51	121
2	64	121
3	70	121
4	73	121
5	72	121

end163.0ms (2.1%)

Compiler: Compiled 387 to 213 computations (45% saved)

Details

analyze1.0s (13.1%)

sample1.2s (15.6%)

simplify94.0ms (1.2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series143.0ms (1.8%)

rewrite68.0ms (0.9%)

simplify188.0ms (2.4%)

prune335.0ms (4.3%)

localize14.0ms (0.2%)

series178.0ms (2.3%)

rewrite18.0ms (0.2%)

simplify151.0ms (2%)

prune371.0ms (4.8%)

localize19.0ms (0.3%)

series127.0ms (1.6%)

rewrite27.0ms (0.3%)

simplify142.0ms (1.8%)

prune392.0ms (5.1%)

localize16.0ms (0.2%)

series172.0ms (2.2%)

rewrite20.0ms (0.3%)

simplify127.0ms (1.6%)

prune390.0ms (5%)

regimes2.3s (30.1%)

bsearch13.0ms (0.2%)

simplify6.0ms (0.1%)

end163.0ms (2.1%)

Profiling