Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample19.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify111.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5574	20

prune3.0ms (0.2%)

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 26 to 20 computations (23.1% saved)

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

rewrite56.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`distribute-lft-out_binary64`
15×	`log-prod_binary64`
12×	`div-inv_binary64`
11×	`add-cube-cbrt_binary64`
6×	`distribute-rgt-out_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `log-div_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `add-cbrt-cube_binary64` `distribute-rgt1-in_binary64` `flip-+_binary64`
1×	`rem-log-exp_binary64` `log-pow_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 51

Calls

2 calls:

27.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
24.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

series154.0ms (9.1%)

Counts

2 → 6

Calls

2 calls:

99.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
55.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

simplify72.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4914	1387
1	4914	1387

prune60.0ms (3.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	1	58

Merged error: 0b

Counts

58 → 1

Compiler

Compiled 1112 to 716 computations (35.6% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

rewrite37.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
13×	`associate-r_binary64`
11×	`add-cube-cbrt_binary64` `times-frac_binary64`
8×	`pow1_binary64` `add-cbrt-cube_binary64`
6×	`prod-exp_binary64` `log-div_binary64`
5×	`flip3-+_binary64` `add-log-exp_binary64` `associate-l_binary64` `flip-+_binary64`
4×	`distribute-lft-out_binary64` `rem-log-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `log-pow_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
1×	`log-prod_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 74

Calls

3 calls:

14.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
10.0ms	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
6.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

series371.0ms (22.1%)

Counts

3 → 9

Calls

3 calls:

288.0ms	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
53.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
30.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify66.0ms (4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4896	1561
1	4896	1561

prune85.0ms (5.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	1	84

Merged error: 0b

Counts

84 → 1

Compiler

Compiled 1500 to 1030 computations (31.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms (0%)

sample619.0ms (36.9%)

Algorithm

1×

intervals

Results

447.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 40 to 34 computations (15% saved)

Details

analyze5.0ms (0.3%)

sample19.0ms (1.1%)

simplify111.0ms (6.6%)

prune3.0ms (0.2%)

localize9.0ms (0.5%)

rewrite56.0ms (3.4%)

series154.0ms (9.1%)

simplify72.0ms (4.3%)

prune60.0ms (3.6%)

localize9.0ms (0.5%)

rewrite37.0ms (2.2%)

series371.0ms (22.1%)

simplify66.0ms (4%)

prune85.0ms (5.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample619.0ms (36.9%)

Profiling