Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify225.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	461	10
1	461	10

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_419`
28×	`add-sqr-sqrt_binary64_441`
24×	`times-frac_binary64_425`
13×	`add-cube-cbrt_binary64_454`
10×	`difference-of-squares_binary64_388`
7×	`distribute-lft-out_binary64_370`
6×	`associate-/r*_binary64_363`
5×	`distribute-lft-out--_binary64_371`
4×	`associate-/l*_binary64_364`
3×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
2×	`associate-/r/_binary64_365` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `add-log-exp_binary64_458` `div-inv_binary64_416` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip-+_binary64_393` `flip--_binary64_394` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

1 → 50

Calls

1 calls:

15.0ms

(/.f64 (+.f64 x 1) (-.f64 1 x))

series24.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

24.0ms

(/.f64 (+.f64 x 1) (-.f64 1 x))

simplify134.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4926	942
1	4926	942

prune93.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 0b

Counts

54 → 4

Compiler

Compiled 815 to 613 computations (24.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))
0.0b	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))

rewrite199.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

365×	`*-un-lft-identity_binary64_419`
270×	`cbrt-prod_binary64_450`
222×	`times-frac_binary64_425`
213×	`add-sqr-sqrt_binary64_441`
93×	`add-cube-cbrt_binary64_454`
64×	`difference-of-squares_binary64_388`
62×	`distribute-lft-out_binary64_370`
57×	`swap-sqr_binary64_386`
44×	`distribute-lft-out--_binary64_371`
33×	`associate-r_binary64_359` `associate-l_binary64_360`
14×	`associate-/r/_binary64_365`
11×	`pow1_binary64_480`
9×	`pow1/3_binary64_501` `unswap-sqr_binary64_387`
7×	`cbrt-div_binary64_451` `div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394`
6×	`add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
2×	`pow-prod-down_binary64_490` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
1×	`associate-l/_binary64_362` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `pow-plus_binary64_482` `*-commutative_binary64_350` `pow2_binary64_500`

Counts

4 → 270

Calls

4 calls:

79.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))
14.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
14.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
14.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))

series209.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))
54.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
48.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
46.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))

simplify247.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5710	8157

prune1.3s (14.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	282	0	282
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	282	4	286

Merged error: 0b

Counts

286 → 4

Compiler

Compiled 9977 to 7812 computations (21.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(/.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)))
0.1b	(/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x)))

rewrite255.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

774×	`times-frac_binary64_425`
762×	`*-un-lft-identity_binary64_419`
564×	`add-sqr-sqrt_binary64_441`
540×	`sqrt-prod_binary64_435`
292×	`add-cube-cbrt_binary64_454`
180×	`difference-of-squares_binary64_388`
100×	`distribute-lft-out_binary64_370`
90×	`distribute-lft-out--_binary64_371`
46×	`associate-/l*_binary64_364`
28×	`sqrt-div_binary64_436`
24×	`associate-/r/_binary64_365`
18×	`associate-/r*_binary64_363`
14×	`flip3--_binary64_423` `flip--_binary64_394`
12×	`div-inv_binary64_416`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`associate-/l/_binary64_366`
2×	`clear-num_binary64_418` `pow1/2_binary64_499` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `flip-+_binary64_393`

Counts

4 → 547

Calls

4 calls:

52.0ms	(/.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)))
16.0ms	(/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x)))
6.0ms	(sqrt.f64 (-.f64 1 x))
6.0ms	(sqrt.f64 (-.f64 1 x))

series123.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x)))
27.0ms	(sqrt.f64 (-.f64 1 x))
26.0ms	(sqrt.f64 (-.f64 1 x))
26.0ms	(/.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)))

simplify428.0ms (5%)

Algorithm

1×	egg-herbie

Counts

559 → 559

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	5330	18190

prune2.1s (24.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	559	0	559
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	559	4	563

Merged error: 0b

Counts

563 → 4

Compiler

Compiled 13444 to 10501 computations (21.9% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1)))

rewrite201.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

714×	`times-frac_binary64_425`
682×	`*-un-lft-identity_binary64_419`
474×	`add-sqr-sqrt_binary64_441`
416×	`sqrt-prod_binary64_435`
282×	`add-cube-cbrt_binary64_454`
128×	`difference-of-squares_binary64_388`
104×	`distribute-lft-out_binary64_370`
64×	`distribute-lft-out--_binary64_371`
55×	`associate-/r*_binary64_363`
20×	`sqrt-div_binary64_436`
19×	`associate-/r/_binary64_365`
13×	`associate-/l*_binary64_364`
10×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
2×	`clear-num_binary64_418` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `pow1_binary64_480`
1×	`flip3--_binary64_423` `flip--_binary64_394` `div-sub_binary64_424`

Counts

2 → 480

Calls

2 calls:

40.0ms	(/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1))))
16.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1)))

series77.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1)))
24.0ms	(/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1))))

simplify379.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5394	15249

prune1.5s (17.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	486	0	486
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	486	4	490

Merged error: 0b

Counts

490 → 4

Compiler

Compiled 11148 to 8723 computations (21.8% saved)

regimes74.0ms (0.9%)

Compiler: Compiled 320 to 266 computations (16.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms (0%)

sample862.0ms (10.2%)

Algorithm

1×

intervals

Results

315.0ms

8000×

body

128

valid

Compiler

Compiled 167 to 140 computations (16.2% saved)

Details

analyze6.0ms (0.1%)

sample19.0ms (0.2%)

simplify225.0ms (2.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite23.0ms (0.3%)

series24.0ms (0.3%)

simplify134.0ms (1.6%)

prune93.0ms (1.1%)

localize16.0ms (0.2%)

rewrite199.0ms (2.4%)

series209.0ms (2.5%)

simplify247.0ms (2.9%)

prune1.3s (14.9%)

localize12.0ms (0.1%)

rewrite255.0ms (3%)

series123.0ms (1.4%)

simplify428.0ms (5%)

prune2.1s (24.6%)

localize12.0ms (0.1%)

rewrite201.0ms (2.4%)

series77.0ms (0.9%)

simplify379.0ms (4.5%)

prune1.5s (17.7%)

regimes74.0ms (0.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample862.0ms (10.2%)

Profiling