Details

analyze1.1s (18.9%)

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)

sample117.0ms (2%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify94.0ms (1.6%)

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)

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 y z) x)
✓	0.2b	(/.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))

series186.0ms (3.3%)

Counts

4 → 153

Calls

4 calls:

81.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
50.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
49.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
5.0ms	(-.f64 (*.f64 y z) x)

rewrite39.0ms (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:

13.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
10.0ms	(+.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)

simplify154.0ms (2.7%)

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

prune362.0ms (6.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	292	8	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	293	8	301

Error

0.0b

Counts

301 → 8

Alt Table

Status	Error	Program
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	36.2b	(/.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (sqrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	31.6b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))
	21.5b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (*.f64 t z) x))) (fma.f64 x x -1)) (-.f64 x 1))
	6.6b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.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)))
	6.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 10974 to 4079 computations (62.8% saved)

localize13.0ms (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)))
✓	2.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	6.1b	(/.f64 z (-.f64 (*.f64 t z) x))

series142.0ms (2.5%)

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 z (-.f64 (*.f64 t z) x))
21.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
8.0ms	(/.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:

7.0ms	(/.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)))

simplify159.0ms (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

prune371.0ms (6.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	262	9	271

Error

Counts

271 → 9

Alt Table

Status	Error	Program
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	36.2b	(/.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (sqrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	21.5b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (*.f64 t z) x))) (fma.f64 x x -1)) (-.f64 x 1))
	22.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	18.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 t) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
▶	6.6b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.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)))
	6.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 10456 to 4040 computations (61.4% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x)))
✓	0.2b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
✓	8.3b	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

series195.0ms (3.4%)

Counts

3 → 144

Calls

3 calls:

85.0ms

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

61.0ms

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

48.0ms

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

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 90

Calls

3 calls:

13.0ms

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

6.0ms

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

4.0ms

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

simplify152.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

417×	`times-frac_binary64`
316×	`associate-/l*_binary64`
295×	`associate-+r+_binary64`
289×	`associate--l+_binary64`
270×	`associate-+l+_binary64`

Counts

234 → 257

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	397	10040
1	1249	9364
2	5188	9364

prune276.0ms (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	257	9	266

Error

Counts

266 → 9

Alt Table

Status	Error	Program
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	36.2b	(/.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (sqrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	21.5b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (*.f64 t z) x))) (fma.f64 x x -1)) (-.f64 x 1))
	22.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	18.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 t) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	6.6b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.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)))
▶	6.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 9911 to 3756 computations (62.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.2b	(/.f64 1 (-.f64 (*.f64 t z) x))
✓	0.2b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
✓	8.3b	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))

series158.0ms (2.8%)

Counts

3 → 132

Calls

3 calls:

86.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
51.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
22.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 116

Calls

3 calls:

14.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
6.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

simplify180.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

436×	`times-frac_binary64`
423×	`fma-neg_binary64`
326×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`
243×	`associate-+l+_binary64`

Counts

248 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	9431
1	1270	8756
2	4988	8754
3	5353	8754

prune355.0ms (6.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	301	9	310

Error

Counts

310 → 9

Alt Table

Status	Error	Program
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	36.2b	(/.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (sqrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	21.5b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (*.f64 t z) x))) (fma.f64 x x -1)) (-.f64 x 1))
	22.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	18.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 t) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	6.6b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.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)))
✓	6.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 10798 to 4550 computations (57.9% saved)

regimes653.0ms (11.4%)

Accuracy

Total 1.9b remaining (99.2%)

Threshold costs 0b (0%)

Counts

111 → 1

Compiler

Compiled 14012 to 8494 computations (39.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	23	38
2	31	38
3	35	38
4	37	38
5	36	38

end1.0ms (0%)

Compiler: Compiled 30 to 16 computations (46.7% saved)

sample894.0ms (15.7%)

Algorithm

1×

intervals

Results

466.0ms	8000×	body	128	valid
17.0ms	314×	body	128	invalid

Compiler

Compiled 291 to 173 computations (40.5% saved)

Details

analyze1.1s (18.9%)

sample117.0ms (2%)

simplify94.0ms (1.6%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series186.0ms (3.3%)

rewrite39.0ms (0.7%)

simplify154.0ms (2.7%)

prune362.0ms (6.3%)

localize13.0ms (0.2%)

series142.0ms (2.5%)

rewrite19.0ms (0.3%)

simplify159.0ms (2.8%)

prune371.0ms (6.5%)

localize13.0ms (0.2%)

series195.0ms (3.4%)

rewrite32.0ms (0.6%)

simplify152.0ms (2.7%)

prune276.0ms (4.8%)

localize11.0ms (0.2%)

series158.0ms (2.8%)

rewrite34.0ms (0.6%)

simplify180.0ms (3.2%)

prune355.0ms (6.2%)

regimes653.0ms (11.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample894.0ms (15.7%)

Profiling