Details

analyze1.0s (19%)

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)

sample31.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify96.0ms (1.7%)

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

6.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.9b	(/.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)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.2b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	10.5b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series204.0ms (3.7%)

Counts

4 → 153

Calls

4 calls:

91.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
54.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
53.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 t z) x)

rewrite40.0ms (0.7%)

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:

15.0ms	(/.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)))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify161.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

268 → 293

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	10265
1	1359	9717
2	5098	9717

prune272.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	287	6	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Error

0.0b

Counts

294 → 6

Alt Table

Status	Error	Program
	17.4b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
▶	1.5b	(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)))
	6.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	15.4b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	7.2b	(/.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))

Compiler

Compiled 10724 to 3960 computations (63.1% saved)

localize12.0ms (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)))
✓	4.9b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.8b	(/.f64 z (-.f64 (*.f64 t z) x))

series139.0ms (2.5%)

Counts

4 → 144

Calls

4 calls:

85.0ms	(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)))
22.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
22.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
9.0ms	(/.f64 y (+.f64 x 1))

rewrite17.0ms (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 x (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 z (-.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)))

simplify152.0ms (2.8%)

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

prune270.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	263	6	269

Error

0.0b

Counts

269 → 6

Alt Table

Status	Error	Program
	17.4b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
✓	1.5b	(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)))
▶	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 z (/.f64 1 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	6.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	15.1b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 10292 to 3946 computations (61.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 z (/.f64 1 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	0.5b	(/.f64 1 (-.f64 (*.f64 t z) x))
	4.9b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.4b	(.f64 z (/.f64 1 (-.f64 (.f64 t z) x)))

series125.0ms (2.3%)

Counts

3 → 120

Calls

3 calls:

84.0ms

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

20.0ms

(*.f64 z (/.f64 1 (-.f64 (*.f64 t z) x)))

20.0ms

(/.f64 1 (-.f64 (*.f64 t z) x))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 85

Calls

3 calls:

8.0ms

(*.f64 z (/.f64 1 (-.f64 (*.f64 t z) x)))

4.0ms

(/.f64 1 (-.f64 (*.f64 t z) x))

0.0ms

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

simplify177.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

390×	`times-frac_binary64`
317×	`fma-neg_binary64`
298×	`sub-neg_binary64`
271×	`associate-/r*_binary64`
271×	`associate-/l*_binary64`

Counts

205 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	310	6917
1	940	6467
2	4161	6390
3	4978	6389
4	5024	6389

prune281.0ms (5.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	284	6	290

Error

0.0b

Counts

290 → 6

Alt Table

Status	Error	Program
	17.4b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
✓	1.5b	(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)))
✓	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 z (/.f64 1 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
▶	6.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	15.1b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 11561 to 4827 computations (58.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.2b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))
✓	10.5b	(/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x))

series179.0ms (3.2%)

Counts

3 → 144

Calls

3 calls:

82.0ms

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

49.0ms

(/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x))

48.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

18.0ms

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

9.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

7.0ms

(/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x))

simplify183.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary64`
389×	`associate-/l*_binary64`
324×	`associate-/r*_binary64`
266×	`associate--l+_binary64`
179×	`sub-neg_binary64`

Counts

311 → 360

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	480	13006
1	1499	12060
2	5108	12060

prune377.0ms (6.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	386	1	387
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	386	7	393

Error

0.0b

Counts

393 → 7

Alt Table

Status	Error	Program
	17.4b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
✓	1.5b	(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)))
✓	1.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 z (/.f64 1 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	6.9b	(/.f64 (+.f64 x (/.f64 (/.f64 1 (-.f64 (.f64 t z) x)) (/.f64 1 (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	6.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.6b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	15.1b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 14390 to 5523 computations (61.6% saved)

regimes704.0ms (12.8%)

Accuracy

Total 0.6b remaining (97.2%)

Threshold costs 0.6b (97.2%)

Counts

133 → 2

Compiler

Compiled 15935 to 9842 computations (38.2% saved)

bsearch5.0ms (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	31	102
1	47	102
2	60	102
3	66	102
4	69	102
5	68	102

end1.0ms (0%)

Compiler: Compiled 73 to 40 computations (45.2% saved)

sample930.0ms (16.9%)

Algorithm

1×

intervals

Results

487.0ms	8000×	body	128	valid
19.0ms	325×	body	128	invalid

Compiler

Compiled 277 to 167 computations (39.7% saved)

Details

analyze1.0s (19%)

sample31.0ms (0.6%)

simplify96.0ms (1.7%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series204.0ms (3.7%)

rewrite40.0ms (0.7%)

simplify161.0ms (2.9%)

prune272.0ms (4.9%)

localize12.0ms (0.2%)

series139.0ms (2.5%)

rewrite17.0ms (0.3%)

simplify152.0ms (2.8%)

prune270.0ms (4.9%)

localize15.0ms (0.3%)

series125.0ms (2.3%)

rewrite19.0ms (0.4%)

simplify177.0ms (3.2%)

prune281.0ms (5.1%)

localize12.0ms (0.2%)

series179.0ms (3.2%)

rewrite51.0ms (0.9%)

simplify183.0ms (3.3%)

prune377.0ms (6.8%)

regimes704.0ms (12.8%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample930.0ms (16.9%)

Profiling