Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample12.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify178.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_2487`
26×	`add-sqr-sqrt_binary64_2509`
21×	`distribute-lft-out_binary64_2438`
18×	`times-frac_binary64_2493`
15×	`add-cube-cbrt_binary64_2522`
14×	`sqrt-prod_binary64_2503`
6×	`associate-/r*_binary64_2431`
5×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `add-log-exp_binary64_2526`
4×	`pow1_binary64_2548`
3×	`associate-/l*_binary64_2432` `flip-+_binary64_2461` `flip3-+_binary64_2490`
2×	`associate-/r/_binary64_2433` `sqrt-div_binary64_2504`
1×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `sqrt-pow1_binary64_2505` `+-commutative_binary64_2417` `sum-log_binary64_2578` `div-exp_binary64_2538` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567` `cbrt-undiv_binary64_2521`

Counts

3 → 71

Calls

3 calls:

10.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series180.0ms (6%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
30.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5025	1543

prune184.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

Compiler

Compiled 2804 to 2217 computations (20.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))

rewrite56.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_2503`
70×	`add-sqr-sqrt_binary64_2509`
46×	`*-un-lft-identity_binary64_2487`
40×	`sqrt-pow1_binary64_2505`
32×	`sqrt-div_binary64_2504`
31×	`pow1_binary64_2548`
28×	`add-cube-cbrt_binary64_2522`
20×	`pow1/2_binary64_2567`
18×	`swap-sqr_binary64_2454`
12×	`rem-sqrt-square_binary64_2500`
10×	`associate-l_binary64_2428` `associate-r_binary64_2427`
9×	`unswap-sqr_binary64_2455` `times-frac_binary64_2493` `flip-+_binary64_2461` `pow-prod-up_binary64_2557` `flip3-+_binary64_2490`
8×	`add-exp-log_binary64_2525` `distribute-lft-out_binary64_2438` `add-cbrt-cube_binary64_2523`
5×	`pow-sqr_binary64_2460` `pow-prod-down_binary64_2558`
4×	`sqr-abs_binary64_2502` `frac-times_binary64_2497` `add-log-exp_binary64_2526`
3×	`associate-/r_binary64_2431` `associate-/l_binary64_2432`
2×	`associate-l/_binary64_2430` `associate-/r/_binary64_2433` `associate-r/_binary64_2429`
1×	`*-commutative_binary64_2418` `prod-exp_binary64_2536` `frac-2neg_binary64_2498` `pow-plus_binary64_2550` `rem-square-sqrt_binary64_2499` `clear-num_binary64_2486` `div-inv_binary64_2484` `pow2_binary64_2568` `cbrt-unprod_binary64_2520` `div-exp_binary64_2538` `sqrt-unprod_binary64_2507` `cbrt-undiv_binary64_2521`

Counts

4 → 165

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
5.0ms	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))

series257.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
53.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
42.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
33.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5003	2567

prune195.0ms (6.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	177	4	181

Merged error: 0b

Counts

181 → 4

Compiler

Compiled 3208 to 2546 computations (20.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
0.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

rewrite57.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`*-un-lft-identity_binary64_2487`
156×	`times-frac_binary64_2493`
114×	`add-sqr-sqrt_binary64_2509`
79×	`add-cube-cbrt_binary64_2522`
69×	`distribute-lft-out_binary64_2438`
38×	`sqrt-prod_binary64_2503`
25×	`associate-/r*_binary64_2431`
17×	`add-exp-log_binary64_2525`
11×	`add-cbrt-cube_binary64_2523`
9×	`associate-/l*_binary64_2432`
8×	`div-exp_binary64_2538`
6×	`div-inv_binary64_2484` `pow1_binary64_2548` `add-log-exp_binary64_2526`
4×	`cbrt-undiv_binary64_2521`
3×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
2×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `sqrt-div_binary64_2504` `rec-exp_binary64_2537` `associate-/l/_binary64_2434` `1-exp_binary64_2531`
1×	`associate-/r/_binary64_2433` `pow-flip_binary64_2561` `sqrt-pow1_binary64_2505` `+-commutative_binary64_2417` `sum-log_binary64_2578` `inv-pow_binary64_2572` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567`

Counts

4 → 183

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
12.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series245.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
68.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
30.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
24.0ms	(sqrt.f64 (+.f64 x 1))

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5404	4258

prune212.0ms (7.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	195	4	199

Merged error: 0b

Counts

199 → 4

Compiler

Compiled 3547 to 2665 computations (24.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite65.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64_2487`
92×	`add-sqr-sqrt_binary64_2509`
79×	`sqrt-prod_binary64_2503`
76×	`times-frac_binary64_2493`
57×	`distribute-lft-out_binary64_2438`
47×	`add-cube-cbrt_binary64_2522`
42×	`associate-r_binary64_2427`
11×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
7×	`pow1_binary64_2548`
6×	`unswap-sqr_binary64_2455` `associate-/r_binary64_2431` `associate-/l_binary64_2432` `add-log-exp_binary64_2526` `associate-l_binary64_2428`
4×	`associate-/r/_binary64_2433` `flip-+_binary64_2461` `flip3-+_binary64_2490`
2×	`prod-exp_binary64_2536` `div-inv_binary64_2484` `cbrt-unprod_binary64_2520` `div-exp_binary64_2538` `sqrt-div_binary64_2504` `cbrt-undiv_binary64_2521`
1×	`-commutative_binary64_2418` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `sqrt-pow1_binary64_2505` `+-commutative_binary64_2417` `sum-log_binary64_2578` `pow-prod-down_binary64_2558` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567` `associate-r/_binary64_2429`

Counts

4 → 160

Calls

4 calls:

25.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
11.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series361.0ms (12%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
118.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
28.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify97.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4951	3818
1	4951	3818

prune186.0ms (6.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	172	4	176

Merged error: 0b

Counts

176 → 4

Compiler

Compiled 3642 to 2305 computations (36.7% saved)

regimes24.0ms (0.8%)

Compiler: Compiled 108 to 92 computations (14.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample420.0ms (14%)

Algorithm

1×

intervals

Results

225.0ms	7997×	body	128	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 62 to 54 computations (12.9% saved)

Details

analyze3.0ms (0.1%)

sample12.0ms (0.4%)

simplify178.0ms (5.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite26.0ms (0.9%)

series180.0ms (6%)

simplify57.0ms (1.9%)

prune184.0ms (6.1%)

localize7.0ms (0.2%)

rewrite56.0ms (1.9%)

series257.0ms (8.6%)

simplify75.0ms (2.5%)

prune195.0ms (6.5%)

localize6.0ms (0.2%)

rewrite57.0ms (1.9%)

series245.0ms (8.1%)

simplify85.0ms (2.8%)

prune212.0ms (7.1%)

localize7.0ms (0.2%)

rewrite65.0ms (2.2%)

series361.0ms (12%)

simplify97.0ms (3.2%)

prune186.0ms (6.2%)

regimes24.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample420.0ms (14%)

Profiling