Details

analyze255.0ms (8%)

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)

sample56.0ms (1.7%)

Algorithm

1×

intervals

Results

19.0ms	132×	body	2048	nan
11.0ms	68×	body	1024	nan
10.0ms	256×	body	128	valid
4.0ms	46×	body	512	nan
1.0ms	12×	body	256	nan
1.0ms	22×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify234.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune2.0ms (0.1%)

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

Error

33.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
31.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_3488`
7×	`add-sqr-sqrt_binary64_3510`
6×	`sqrt-prod_binary64_3504`
5×	`add-cube-cbrt_binary64_3523` `add-log-exp_binary64_3527` `pow1_binary64_3549`
4×	`add-exp-log_binary64_3526` `log-prod_binary64_3574`
3×	`add-cbrt-cube_binary64_3524`
2×	`difference-of-squares_binary64_3457` `distribute-lft-out_binary64_3439` `sqrt-div_binary64_3505` `flip-+_binary64_3462` `flip3-+_binary64_3491` `log-div_binary64_3575`
1×	`rem-log-exp_binary64_3529` `log-pow_binary64_3577` `flip3--_binary64_3492` `difference-of-sqr-1_binary64_3458` `+-commutative_binary64_3418` `pow1/2_binary64_3568` `flip--_binary64_3463` `sqrt-pow1_binary64_3506` `sum-log_binary64_3579` `rem-sqrt-square_binary64_3501`

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))

series95.0ms (3%)

Counts

3 → 9

Calls

3 calls:

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

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4931	923
1	4931	923

prune51.0ms (1.6%)

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

Error

Counts

55 → 2

Compiler

Compiled 841 to 558 computations (33.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3510`
15×	`sqrt-prod_binary64_3504`
13×	`*-un-lft-identity_binary64_3488`
12×	`sqrt-div_binary64_3505`
10×	`associate-r_binary64_3428`
8×	`add-cube-cbrt_binary64_3523` `pow1_binary64_3549`
7×	`associate-l_binary64_3429`
6×	`add-exp-log_binary64_3526`
5×	`add-cbrt-cube_binary64_3524` `flip-+_binary64_3462` `flip3-+_binary64_3491` `add-log-exp_binary64_3527`
4×	`unswap-sqr_binary64_3456` `frac-times_binary64_3498`
3×	`flip3--_binary64_3492` `log-prod_binary64_3574` `pow-prod-down_binary64_3559` `flip--_binary64_3463`
2×	`difference-of-squares_binary64_3457` `associate-l/_binary64_3431` `associate-r/_binary64_3430` `log-div_binary64_3575` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506`
1×	`rem-log-exp_binary64_3529` `distribute-lft-out_binary64_3439` `log-pow_binary64_3577` `distribute-lft-out--_binary64_3440` `difference-of-sqr-1_binary64_3458` `cbrt-unprod_binary64_3521` `+-commutative_binary64_3418` `*-commutative_binary64_3419` `sum-log_binary64_3579` `sqrt-unprod_binary64_3508` `prod-exp_binary64_3537`

Counts

3 → 68

Calls

3 calls:

13.0ms	(*.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))))

series109.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
38.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
28.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4977	1681
1	4977	1681

prune85.0ms (2.6%)

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

Error

Counts

79 → 2

Compiler

Compiled 1528 to 1158 computations (24.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
0.0b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
31.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))
31.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sqrt-prod_binary64_3504`
16×	`*-un-lft-identity_binary64_3488`
14×	`add-sqr-sqrt_binary64_3510` `log-prod_binary64_3574`
10×	`add-cube-cbrt_binary64_3523` `pow1_binary64_3549`
8×	`sqrt-div_binary64_3505`
6×	`log-pow_binary64_3577` `add-exp-log_binary64_3526`
4×	`difference-of-squares_binary64_3457` `add-cbrt-cube_binary64_3524` `log-div_binary64_3575` `add-log-exp_binary64_3527` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506`
2×	`rem-log-exp_binary64_3529` `distribute-lft-out_binary64_3439` `flip3--_binary64_3492` `flip-+_binary64_3462` `difference-of-sqr-1_binary64_3458` `flip3-+_binary64_3491` `flip--_binary64_3463` `rem-sqrt-square_binary64_3501`

Counts

4 → 76

Calls

4 calls:

8.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
8.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series121.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
39.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
20.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
20.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify94.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4882	1716
1	4882	1716

prune116.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	88	2	90

Error

Counts

90 → 2

Compiler

Compiled 2432 to 1598 computations (34.3% saved)

regimes67.0ms (2.1%)

Accuracy

Total 0.0b remaining (2.7%)

Threshold costs 0.0b (2.7%)

Compiler

Compiled 474 to 360 computations (24.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.7s (52.5%)

Algorithm

1×

intervals

Results

595.0ms	3956×	body	2048	nan
335.0ms	8000×	body	128	valid
239.0ms	2000×	body	1024	nan
92.0ms	1005×	body	512	nan
29.0ms	480×	body	256	nan
15.0ms	490×	body	128	nan
2.0ms	12×	body	4096	nan

Compiler

Compiled 128 to 99 computations (22.7% saved)

Details

analyze255.0ms (8%)

sample56.0ms (1.7%)

simplify234.0ms (7.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite22.0ms (0.7%)

series95.0ms (3%)

simplify59.0ms (1.8%)

prune51.0ms (1.6%)

localize8.0ms (0.3%)

rewrite24.0ms (0.7%)

series109.0ms (3.4%)

simplify77.0ms (2.4%)

prune85.0ms (2.6%)

localize9.0ms (0.3%)

rewrite31.0ms (1%)

series121.0ms (3.8%)

simplify94.0ms (2.9%)

prune116.0ms (3.6%)

regimes67.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (52.5%)

Profiling