Details

analyze991.0ms (14.5%)

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
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 (17.5%)

Results

1.1s	8256×	body	128	valid
48.0ms	318×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify103.0ms (1.5%)

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

6.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.6b	(/.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 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.0b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	8.3b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series206.0ms (3%)

Counts

4 → 153

Calls

4 calls:

92.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
55.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
52.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

13.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
8.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 y z) x)

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
201×	`fma-def_binary64`

Counts

268 → 300

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	10267
1	1359	9717
2	5100	9717

prune301.0ms (4.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	296	5	301

Error

0.0b

Counts

301 → 5

Alt Table

Status	Error	Program
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
	6.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	25.9b	(-.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 y (.f64 t (+.f64 x 1)))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1)))))
	6.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
▶	2.0b	(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)))

Compiler

Compiled 10870 to 3997 computations (63.2% 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)))
✓	1.7b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	6.4b	(/.f64 z (-.f64 (*.f64 t z) x))

series141.0ms (2.1%)

Counts

4 → 144

Calls

4 calls:

88.0ms	(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))

rewrite19.0ms (0.3%)

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:

4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
3.0ms	(/.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)))

simplify139.0ms (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

prune316.0ms (4.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	262	6	268

Error

0.0b

Counts

268 → 6

Alt Table

Status	Error	Program
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
	6.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
▶	2.0b	(fma.f64 (.f64 y (/.f64 1 (+.f64 x 1))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	6.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	18.5b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	2.3b	(fma.f64 (.f64 (/.f64 y (fma.f64 x x -1)) (-.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 10404 to 3982 computations (61.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 y (/.f64 1 (+.f64 x 1))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	0.1b	(*.f64 y (/.f64 1 (+.f64 x 1)))
	1.7b	(/.f64 x (-.f64 (*.f64 t z) x))
	6.4b	(/.f64 z (-.f64 (*.f64 t z) x))

series101.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

91.0ms	(fma.f64 (.f64 y (/.f64 1 (+.f64 x 1))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
9.0ms	(*.f64 y (/.f64 1 (+.f64 x 1)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

8.0ms	(*.f64 y (/.f64 1 (+.f64 x 1)))
0.0ms	(fma.f64 (.f64 y (/.f64 1 (+.f64 x 1))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

797×	`cancel-sign-sub-inv_binary64`
330×	`times-frac_binary64`
302×	`sub-neg_binary64`
300×	`associate-/l*_binary64`
239×	`fma-neg_binary64`

Counts

125 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	4465
1	857	4088
2	3863	4048
3	5486	4048

prune321.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	282	1	283
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	283	6	289

Error

0.0b

Counts

289 → 6

Alt Table

Status	Error	Program
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
	6.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
✓	2.0b	(fma.f64 (.f64 y (/.f64 1 (+.f64 x 1))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	6.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	18.5b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
▶	2.0b	(fma.f64 y (/.f64 (/.f64 z (-.f64 (.f64 t z) x)) (+.f64 1 x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 1 x)))

Compiler

Compiled 11564 to 4700 computations (59.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 z (-.f64 (*.f64 t z) x)) (+.f64 1 x))
✓	0.1b	(fma.f64 y (/.f64 (/.f64 z (-.f64 (.f64 t z) x)) (+.f64 1 x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 1 x)))
	1.7b	(/.f64 x (-.f64 (*.f64 t z) x))
	6.4b	(/.f64 z (-.f64 (*.f64 t z) x))

series228.0ms (3.3%)

Counts

2 → 84

Calls

2 calls:

147.0ms	(fma.f64 y (/.f64 (/.f64 z (-.f64 (.f64 t z) x)) (+.f64 1 x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 1 x)))
81.0ms	(/.f64 (/.f64 z (-.f64 (*.f64 t z) x)) (+.f64 1 x))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`times-frac_binary64`
85×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`distribute-lft-out_binary64`

Counts

2 → 108

Calls

2 calls:

11.0ms	(/.f64 (/.f64 z (-.f64 (*.f64 t z) x)) (+.f64 1 x))
0.0ms	(fma.f64 y (/.f64 (/.f64 z (-.f64 (.f64 t z) x)) (+.f64 1 x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 1 x)))

simplify151.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

881×	`times-frac_binary64`
673×	`associate-/r*_binary64`
569×	`associate-/l*_binary64`
210×	`fma-def_binary64`
186×	`associate-/l/_binary64`

Counts

192 → 257

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	591	11127
1	1888	10291
2	5506	10291

prune756.0ms (11.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	398	1	399
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	399	6	405

Error

0.0b

Counts

405 → 6

Alt Table

Status	Error	Program
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
	6.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
✓	2.0b	(fma.f64 (.f64 y (/.f64 1 (+.f64 x 1))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	6.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	18.5b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 y (fma.f64 x t t)))
✓	2.0b	(fma.f64 y (/.f64 (/.f64 z (-.f64 (.f64 t z) x)) (+.f64 1 x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 1 x)))

Compiler

Compiled 18433 to 7279 computations (60.5% saved)

regimes1.4s (20.2%)

Accuracy

Total 0.6b remaining (96.2%)

Threshold costs 0.6b (96.2%)

Counts

229 → 2

Compiler

Compiled 30433 to 18374 computations (39.6% saved)

bsearch9.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
7×	`*-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	32	102
1	47	102
2	60	102
3	66	102
4	69	102
5	68	102

end115.0ms (1.7%)

Compiler: Compiled 334 to 177 computations (47% saved)

Details

analyze991.0ms (14.5%)

sample1.2s (17.5%)

simplify103.0ms (1.5%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series206.0ms (3%)

rewrite40.0ms (0.6%)

simplify135.0ms (2%)

prune301.0ms (4.4%)

localize14.0ms (0.2%)

series141.0ms (2.1%)

rewrite19.0ms (0.3%)

simplify139.0ms (2%)

prune316.0ms (4.6%)

localize13.0ms (0.2%)

series101.0ms (1.5%)

rewrite12.0ms (0.2%)

simplify97.0ms (1.4%)

prune321.0ms (4.7%)

localize12.0ms (0.2%)

series228.0ms (3.3%)

rewrite22.0ms (0.3%)

simplify151.0ms (2.2%)

prune756.0ms (11.1%)

regimes1.4s (20.2%)

bsearch9.0ms (0.1%)

simplify4.0ms (0.1%)

end115.0ms (1.7%)

Profiling