Details

analyze107.0ms (0.1%)

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 8 to 8 computations (0% saved)

sample1.4s (1%)

Algorithm

1×

intervals

Results

1.4s

256×

body

128

valid

Compiler

Compiled 15 to 16 computations (-6.7% saved)

simplify284.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

prune28.0ms (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: 0.3b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize64.0ms (0%)

Local error

Found 1 expressions with local error:

0.2b	(log.f64 (-.f64 (/.f64 1 x) 1))

rewrite113.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`log-prod_binary64`
11×	`*-un-lft-identity_binary64`
6×	`difference-of-squares_binary64` `times-frac_binary64`
3×	`difference-of-sqr-1_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64` `log-div_binary64`
1×	`add-log-exp_binary64` `flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `flip--_binary64`

Counts

1 → 25

Calls

1 calls:

83.0ms

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

series258.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

255.0ms

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

simplify666.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (503.0ms)

Iter	Nodes	Cost
0	5912	470

prune484.0ms (0.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	20	8	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	9	29

Merged error: 0b

Counts

29 → 9

Compiler

Compiled 501 to 429 computations (14.4% saved)

localize104.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite589.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
45×	`log-prod_binary64`
37×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`
20×	`difference-of-squares_binary64` `associate-+r+_binary64`
13×	`pow1_binary64` `add-exp-log_binary64`
12×	`associate-/r*_binary64`
10×	`difference-of-sqr-1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64` `log-div_binary64` `pow-flip_binary64`
5×	`log-pow_binary64` `associate-+l+_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-+r-_binary64` `pow1/2_binary64` `flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`rem-log-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 165

Calls

4 calls:

213.0ms	(+.f64 (log.f64 (+.f64 1 (/.f64 1 (sqrt.f64 x)))) (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1)))
96.0ms	(log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1))
60.0ms	(/.f64 1 (sqrt.f64 x))
24.0ms	(/.f64 1 (sqrt.f64 x))

series1.4s (0.9%)

Counts

4 → 12

Calls

4 calls:

647.0ms	(+.f64 (log.f64 (+.f64 1 (/.f64 1 (sqrt.f64 x)))) (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1)))
262.0ms	(/.f64 1 (sqrt.f64 x))
243.0ms	(/.f64 1 (sqrt.f64 x))
227.0ms	(log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1))

simplify463.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (292.0ms)

Iter	Nodes	Cost
0	4960	3080
1	4960	3080

prune8.0s (5.3%)

Pruning

38 alts after pruning (36 fresh and 2 done)

	Pruned	Kept	Total
New	146	31	177
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	148	38	186

Merged error: 0b

Counts

186 → 38

Compiler

Compiled 5035 to 3744 computations (25.6% saved)

localize167.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 (log.f64 (sqrt.f64 x)))))) (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1)))
0.0b	(log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1))
0.2b	(/.f64 1 (sqrt.f64 x))
4.8b	(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))

rewrite387.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
50×	`log-prod_binary64`
42×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
20×	`difference-of-squares_binary64` `associate-+r+_binary64`
16×	`exp-prod_binary64`
15×	`pow1_binary64`
11×	`log-pow_binary64`
10×	`difference-of-sqr-1_binary64`
9×	`add-exp-log_binary64`
6×	`associate-/r*_binary64` `distribute-lft-neg-in_binary64` `add-cbrt-cube_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-in_binary64` `exp-sum_binary64` `log-div_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out_binary64`
4×	`associate-+l+_binary64` `distribute-lft-out--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
2×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `associate-+l-_binary64` `rem-exp-log_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`1-exp_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `neg-mul-1_binary64` `exp-diff_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `rec-exp_binary64` `exp-neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 152

Calls

4 calls:

90.0ms	(+.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 (log.f64 (sqrt.f64 x)))))) (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1)))
77.0ms	(log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1))
68.0ms	(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))
59.0ms	(/.f64 1 (sqrt.f64 x))

series3.0s (2%)

Counts

4 → 12

Calls

4 calls:

1.6s	(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))
1.1s	(+.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 (log.f64 (sqrt.f64 x)))))) (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1)))
200.0ms	(log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) 1))
102.0ms	(/.f64 1 (sqrt.f64 x))

simplify342.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (196.0ms)

Iter	Nodes	Cost
0	5011	2904

prune9.8s (6.5%)

Pruning

49 alts after pruning (46 fresh and 3 done)

	Pruned	Kept	Total
New	144	20	164
Fresh	9	26	35
Picked	0	1	1
Done	0	2	2
Total	153	49	202

Merged error: 0b

Counts

202 → 49

Compiler

Compiled 5379 to 3743 computations (30.4% saved)

localize146.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 -1 (/.f64 1 (sqrt.f64 x))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 1 (sqrt.f64 x))
4.8b	(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))

rewrite286.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64`
36×	`times-frac_binary64`
32×	`sqrt-prod_binary64`
16×	`exp-prod_binary64`
13×	`pow1_binary64`
12×	`associate-/r*_binary64` `add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`log-prod_binary64` `log-pow_binary64` `distribute-lft-neg-in_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-in_binary64` `exp-sum_binary64` `associate-/l*_binary64` `pow-flip_binary64`
5×	`add-log-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
4×	`div-exp_binary64`
3×	`div-inv_binary64`
2×	`distribute-lft-out_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `neg-sub0_binary64` `neg-mul-1_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `exp-neg_binary64` `flip-+_binary64`

Counts

4 → 140

Calls

4 calls:

61.0ms	(sqrt.f64 (+.f64 -1 (/.f64 1 (sqrt.f64 x))))
45.0ms	(/.f64 1 (sqrt.f64 x))
33.0ms	(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))
33.0ms	(/.f64 1 (sqrt.f64 x))

series2.2s (1.5%)

Counts

4 → 12

Calls

4 calls:

1.5s	(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))
294.0ms	(/.f64 1 (sqrt.f64 x))
215.0ms	(sqrt.f64 (+.f64 -1 (/.f64 1 (sqrt.f64 x))))
194.0ms	(/.f64 1 (sqrt.f64 x))

simplify544.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (343.0ms)

Iter	Nodes	Cost
0	5047	1778

prune11.2s (7.5%)

Pruning

53 alts after pruning (49 fresh and 4 done)

	Pruned	Kept	Total
New	134	18	152
Fresh	14	31	45
Picked	0	1	1
Done	0	3	3
Total	148	53	201

Merged error: 0b

Counts

201 → 53

Compiler

Compiled 4843 to 3258 computations (32.7% saved)

regimes22.8s (15.3%)

Compiler: Compiled 33853 to 28206 computations (16.7% saved)

bsearch20.9s (14%)

simplify23.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	66	50
1	66	50

end0.0ms (0%)

sample1.1min (42.5%)

Algorithm

1×

intervals

Results

1.8s	8000×	body	128	valid
1.0ms	4×	body	128	nan

Compiler

Compiled 6743 to 5600 computations (17% saved)

Pareto

Details

analyze107.0ms (0.1%)

sample1.4s (1%)

simplify284.0ms (0.2%)

prune28.0ms (0%)

localize64.0ms (0%)

rewrite113.0ms (0.1%)

series258.0ms (0.2%)

simplify666.0ms (0.4%)

prune484.0ms (0.3%)

localize104.0ms (0.1%)

rewrite589.0ms (0.4%)

series1.4s (0.9%)

simplify463.0ms (0.3%)

prune8.0s (5.3%)

localize167.0ms (0.1%)

rewrite387.0ms (0.3%)

series3.0s (2%)

simplify342.0ms (0.2%)

prune9.8s (6.5%)

localize146.0ms (0.1%)

rewrite286.0ms (0.2%)

series2.2s (1.5%)

simplify544.0ms (0.4%)

prune11.2s (7.5%)

regimes22.8s (15.3%)

bsearch20.9s (14%)

simplify23.0ms (0%)

end0.0ms (0%)

sample1.1min (42.5%)

Profiling