Details

analyze255.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample52.0ms (1%)

Algorithm

1×

intervals

Results

20.0ms	131×	body	2048	nan
11.0ms	256×	body	128	valid
6.0ms	54×	body	1024	nan
3.0ms	38×	body	512	nan
1.0ms	13×	body	256	nan
1.0ms	16×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify241.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune2.0ms (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: 28.4b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
26.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_419`
7×	`add-sqr-sqrt_binary64_441`
6×	`sqrt-prod_binary64_435`
5×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1_binary64_480`
4×	`log-prod_binary64_505` `add-exp-log_binary64_457`
3×	`add-cbrt-cube_binary64_455`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `difference-of-squares_binary64_388` `distribute-lft-out_binary64_370` `flip-+_binary64_393` `log-div_binary64_506`
1×	`rem-log-exp_binary64_460` `pow1/2_binary64_499` `difference-of-sqr-1_binary64_389` `sum-log_binary64_510` `flip3--_binary64_423` `log-pow_binary64_508` `sqrt-pow1_binary64_437` `flip--_binary64_394` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

3 → 45

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series119.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
38.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
22.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4931	923
1	4931	923

prune75.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0.0b

Counts

55 → 2

Compiler

Compiled 837 to 557 computations (33.5% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.2b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_441`
15×	`sqrt-prod_binary64_435`
13×	`*-un-lft-identity_binary64_419`
12×	`sqrt-div_binary64_436`
10×	`associate-r_binary64_359`
8×	`add-cube-cbrt_binary64_454` `pow1_binary64_480`
7×	`associate-l_binary64_360`
6×	`add-exp-log_binary64_457`
5×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393` `add-cbrt-cube_binary64_455`
4×	`unswap-sqr_binary64_387` `frac-times_binary64_429`
3×	`pow-prod-down_binary64_490` `log-prod_binary64_505` `flip3--_binary64_423` `flip--_binary64_394`
2×	`associate-l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `associate-r/_binary64_361` `sqrt-pow1_binary64_437` `log-div_binary64_506`
1×	`sqrt-unprod_binary64_439` `rem-log-exp_binary64_460` `difference-of-sqr-1_binary64_389` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `log-pow_binary64_508` `*-commutative_binary64_350` `+-commutative_binary64_349`

Counts

3 → 68

Calls

3 calls:

15.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series106.0ms (2%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
35.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
29.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4977	1681
1	4977	1681

prune83.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0.0b

Counts

79 → 2

Compiler

Compiled 1524 to 1157 computations (24.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
0.1b	(/.f64 3/32 (pow.f64 x 4))
0.1b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.5b	(/.f64 1/4 (*.f64 x x))

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_419`
32×	`add-sqr-sqrt_binary64_441`
26×	`add-cube-cbrt_binary64_454`
25×	`times-frac_binary64_425`
16×	`distribute-lft-out--_binary64_371`
14×	`add-exp-log_binary64_457`
13×	`pow1_binary64_480`
12×	`unpow-prod-down_binary64_498`
11×	`add-cbrt-cube_binary64_455`
10×	`add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385`
9×	`distribute-lft-out_binary64_370` `log-pow_binary64_508`
8×	`associate-/r*_binary64_363`
6×	`log-prod_binary64_505` `associate-/l*_binary64_364`
5×	`diff-log_binary64_511` `div-exp_binary64_470`
4×	`sqr-pow_binary64_391` `associate--r+_binary64_355`
3×	`associate--l+_binary64_356` `difference-of-squares_binary64_388` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `sub-neg_binary64_412` `div-inv_binary64_416` `sum-log_binary64_510` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip--_binary64_394`
1×	`associate--r-_binary64_358` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `associate-+r-_binary64_353`

Counts

4 → 121

Calls

4 calls:

27.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
8.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
5.0ms	(/.f64 3/32 (pow.f64 x 4))
5.0ms	(/.f64 1/4 (*.f64 x x))

series180.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
42.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
22.0ms	(/.f64 3/32 (pow.f64 x 4))
16.0ms	(/.f64 1/4 (*.f64 x x))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4946	2312
1	4946	2312

prune160.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	132	3	135

Merged error: 0b

Counts

135 → 3

Compiler

Compiled 2992 to 2021 computations (32.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (.f64 x x)) (log.f64 x))))) (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))))
0.5b	(/.f64 1/4 (*.f64 x x))
0.5b	(/.f64 1/4 (*.f64 x x))
0.5b	(/.f64 1/4 (*.f64 x x))

rewrite130.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

434×	`*-un-lft-identity_binary64_419`
240×	`distribute-lft-out--_binary64_371`
196×	`cbrt-prod_binary64_450`
131×	`pow1_binary64_480`
120×	`distribute-lft-out_binary64_370` `log-pow_binary64_508`
87×	`swap-sqr_binary64_386`
34×	`add-sqr-sqrt_binary64_441`
21×	`add-exp-log_binary64_457`
19×	`add-cbrt-cube_binary64_455`
18×	`add-cube-cbrt_binary64_454`
15×	`associate-r_binary64_359` `associate-l_binary64_360`
12×	`cbrt-div_binary64_451`
9×	`times-frac_binary64_425` `associate-/l*_binary64_364`
6×	`pow1/3_binary64_501` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-/r*_binary64_363`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
1×	`pow-plus_binary64_482` `*-commutative_binary64_350` `pow2_binary64_500`

Counts

4 → 210

Calls

4 calls:

61.0ms	(.f64 (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (.f64 x x)) (log.f64 x))))) (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))))
5.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 1/4 (*.f64 x x))

series620.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

567.0ms	(.f64 (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (.f64 x x)) (log.f64 x))))) (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))))
19.0ms	(/.f64 1/4 (*.f64 x x))
17.0ms	(/.f64 1/4 (*.f64 x x))
16.0ms	(/.f64 1/4 (*.f64 x x))

simplify125.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5172	8237

prune1.0s (18.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	222	3	225

Merged error: 0b

Counts

225 → 3

Compiler

Compiled 12857 to 9181 computations (28.6% saved)

regimes57.0ms (1.1%)

Compiler: Compiled 477 to 367 computations (23.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.8s (32.8%)

Algorithm

1×

intervals

Results

629.0ms	4059×	body	2048	nan
344.0ms	8000×	body	128	valid
234.0ms	1950×	body	1024	nan
92.0ms	1032×	body	512	nan
28.0ms	461×	body	256	nan
16.0ms	480×	body	128	nan
1.0ms	7×	body	4096	nan

Compiler

Compiled 169 to 132 computations (21.9% saved)

Details

analyze255.0ms (4.7%)

sample52.0ms (1%)

simplify241.0ms (4.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite21.0ms (0.4%)

series119.0ms (2.2%)

simplify94.0ms (1.7%)

prune75.0ms (1.4%)

localize17.0ms (0.3%)

rewrite26.0ms (0.5%)

series106.0ms (2%)

simplify74.0ms (1.4%)

prune83.0ms (1.5%)

localize12.0ms (0.2%)

rewrite55.0ms (1%)

series180.0ms (3.3%)

simplify84.0ms (1.6%)

prune160.0ms (3%)

localize18.0ms (0.3%)

rewrite130.0ms (2.4%)

series620.0ms (11.5%)

simplify125.0ms (2.3%)

prune1.0s (18.6%)

regimes57.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (32.8%)

Profiling