Details

analyze7.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample25.0ms (0.1%)

Algorithm

1×

intervals

Results

6.0ms	40×	body	1024	valid
6.0ms	53×	body	512	valid
5.0ms	133×	body	128	valid
2.0ms	30×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify107.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.5b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite95.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_3147`
74×	`times-frac_binary64_3153`
72×	`add-sqr-sqrt_binary64_3169`
39×	`add-cube-cbrt_binary64_3182`
26×	`cancel-sign-sub-inv_binary64_3113`
18×	`distribute-lft-out--_binary64_3099`
17×	`distribute-lft-out_binary64_3098`
14×	`associate-+l+_binary64_3080` `difference-of-squares_binary64_3116`
12×	`add-exp-log_binary64_3185`
11×	`associate-/r*_binary64_3091` `add-log-exp_binary64_3186`
10×	`div-inv_binary64_3144`
8×	`add-cbrt-cube_binary64_3183`
6×	`pow1_binary64_3208` `associate-/l*_binary64_3092`
4×	`difference-of-sqr-1_binary64_3117` `div-exp_binary64_3198` `associate-/r/_binary64_3093`
3×	`frac-add_binary64_3155` `flip--_binary64_3122` `flip3--_binary64_3151`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `inv-pow_binary64_3232` `sub-neg_binary64_3140` `frac-sub_binary64_3156` `cbrt-undiv_binary64_3181` `pow-flip_binary64_3221` `diff-log_binary64_3239` `1-exp_binary64_3191` `rec-exp_binary64_3197` `sum-log_binary64_3238`
1×	`associate-+l-_binary64_3082` `+-commutative_binary64_3077`

Counts

4 → 161

Calls

4 calls:

46.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
24.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))

series85.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
13.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (-.f64 x 1))
9.0ms	(/.f64 1 (+.f64 x 1))

simplify100.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4963	2797
1	4963	2797

prune522.0ms (1.7%)

Pruning

49 alts after pruning (49 fresh and 0 done)

	Pruned	Kept	Total
New	124	49	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	49	174

Merged error: 0.4b

Counts

174 → 49

Compiler

Compiled 3366 to 2753 computations (18.2% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
3.8b	(+.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))

rewrite100.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_3147`
74×	`times-frac_binary64_3153`
72×	`add-sqr-sqrt_binary64_3169`
39×	`add-cube-cbrt_binary64_3182`
26×	`cancel-sign-sub-inv_binary64_3113`
19×	`distribute-lft-out--_binary64_3099`
16×	`distribute-lft-out_binary64_3098`
14×	`difference-of-squares_binary64_3116` `associate-+r+_binary64_3079`
12×	`add-exp-log_binary64_3185`
11×	`associate-/r*_binary64_3091` `add-log-exp_binary64_3186`
10×	`div-inv_binary64_3144`
8×	`add-cbrt-cube_binary64_3183`
6×	`pow1_binary64_3208` `associate-/l*_binary64_3092`
4×	`difference-of-sqr-1_binary64_3117` `div-exp_binary64_3198` `associate-/r/_binary64_3093`
3×	`frac-add_binary64_3155` `flip--_binary64_3122` `flip3--_binary64_3151`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `inv-pow_binary64_3232` `sub-neg_binary64_3140` `frac-sub_binary64_3156` `cbrt-undiv_binary64_3181` `pow-flip_binary64_3221` `diff-log_binary64_3239` `1-exp_binary64_3191` `rec-exp_binary64_3197` `sum-log_binary64_3238`
1×	`associate-+r-_binary64_3081` `+-commutative_binary64_3077`

Counts

4 → 161

Calls

4 calls:

41.0ms	(+.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))
29.0ms	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))

series77.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(+.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))
14.0ms	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (-.f64 x 1))
9.0ms	(/.f64 1 (+.f64 x 1))

simplify82.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4908	2842
1	4908	2842

prune784.0ms (2.6%)

Pruning

72 alts after pruning (71 fresh and 1 done)

	Pruned	Kept	Total
New	120	53	173
Fresh	30	18	48
Picked	0	1	1
Done	0	0	0
Total	150	72	222

Merged error: 0.4b

Counts

222 → 72

Compiler

Compiled 4292 to 3507 computations (18.3% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 1 x))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
3.8b	(+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))

rewrite103.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_3147`
74×	`times-frac_binary64_3153`
72×	`add-sqr-sqrt_binary64_3169`
39×	`add-cube-cbrt_binary64_3182`
26×	`cancel-sign-sub-inv_binary64_3113`
19×	`distribute-lft-out--_binary64_3099`
16×	`distribute-lft-out_binary64_3098`
14×	`difference-of-squares_binary64_3116` `associate-+r+_binary64_3079`
12×	`add-exp-log_binary64_3185`
11×	`associate-/r*_binary64_3091` `add-log-exp_binary64_3186`
10×	`div-inv_binary64_3144`
8×	`add-cbrt-cube_binary64_3183`
6×	`pow1_binary64_3208` `associate-/l*_binary64_3092`
4×	`difference-of-sqr-1_binary64_3117` `div-exp_binary64_3198` `associate-/r/_binary64_3093`
3×	`frac-add_binary64_3155` `flip--_binary64_3122` `flip3--_binary64_3151`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `inv-pow_binary64_3232` `sub-neg_binary64_3140` `frac-sub_binary64_3156` `cbrt-undiv_binary64_3181` `pow-flip_binary64_3221` `diff-log_binary64_3239` `1-exp_binary64_3191` `rec-exp_binary64_3197` `sum-log_binary64_3238`
1×	`associate-+r-_binary64_3081` `+-commutative_binary64_3077`

Counts

4 → 161

Calls

4 calls:

51.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))
25.0ms	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 1 x))

series87.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))
17.0ms	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (+.f64 1 x))
8.0ms	(/.f64 1 (-.f64 x 1))

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4917	2842
1	4917	2842

prune1.3s (4.1%)

Pruning

109 alts after pruning (107 fresh and 2 done)

	Pruned	Kept	Total
New	124	49	173
Fresh	12	58	70
Picked	0	1	1
Done	0	1	1
Total	136	109	245

Merged error: 0.4b

Counts

245 → 109

Compiler

Compiled 5882 to 4937 computations (16.1% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 1) (+.f64 1 x))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
3.8b	(+.f64 (/.f64 (sqrt.f64 1) (+.f64 1 x)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))

rewrite112.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`*-un-lft-identity_binary64_3147`
86×	`times-frac_binary64_3153`
80×	`add-sqr-sqrt_binary64_3169`
47×	`add-cube-cbrt_binary64_3182`
26×	`cancel-sign-sub-inv_binary64_3113`
17×	`distribute-lft-out--_binary64_3099`
16×	`distribute-lft-out_binary64_3098`
15×	`sqrt-prod_binary64_3163`
14×	`difference-of-squares_binary64_3116` `associate-+r+_binary64_3079`
11×	`associate-/r*_binary64_3091` `add-log-exp_binary64_3186`
10×	`add-exp-log_binary64_3185`
9×	`associate-/l*_binary64_3092`
8×	`add-cbrt-cube_binary64_3183`
6×	`div-inv_binary64_3144`
5×	`pow1_binary64_3208`
4×	`difference-of-sqr-1_binary64_3117` `associate-/r/_binary64_3093`
3×	`frac-add_binary64_3155` `flip--_binary64_3122` `flip3--_binary64_3151` `div-exp_binary64_3198`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `sub-neg_binary64_3140` `frac-sub_binary64_3156` `cbrt-undiv_binary64_3181` `diff-log_binary64_3239` `sum-log_binary64_3238`
1×	`inv-pow_binary64_3232` `associate-+r-_binary64_3081` `+-commutative_binary64_3077` `pow-flip_binary64_3221` `1-exp_binary64_3191` `rec-exp_binary64_3197`

Counts

4 → 169

Calls

4 calls:

56.0ms	(+.f64 (/.f64 (sqrt.f64 1) (+.f64 1 x)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))
25.0ms	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 (sqrt.f64 1) (+.f64 1 x))
7.0ms	(/.f64 1 (-.f64 x 1))

series90.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(+.f64 (/.f64 (sqrt.f64 1) (+.f64 1 x)) (-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x)))
14.0ms	(-.f64 (/.f64 1 (-.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (-.f64 x 1))
8.0ms	(/.f64 (sqrt.f64 1) (+.f64 1 x))

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4941	2990
1	4941	2990

prune900.0ms (2.9%)

Pruning

127 alts after pruning (124 fresh and 3 done)

	Pruned	Kept	Total
New	150	31	181
Fresh	13	93	106
Picked	0	1	1
Done	0	2	2
Total	163	127	290

Merged error: 0.4b

Counts

290 → 127

Compiler

Compiled 2916 to 2433 computations (16.6% saved)

regimes2.1s (6.7%)

Compiler: Compiled 17127 to 14807 computations (13.5% saved)

bsearch14.7s (47.9%)

Compiler: Compiled 15 to 13 computations (13.3% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	157	141
1	157	141

end0.0ms (0%)

sample9.1s (29.7%)

Algorithm

1×

intervals

Results

186.0ms	1257×	body	1024	valid
178.0ms	4502×	body	128	valid
167.0ms	1491×	body	512	valid
60.0ms	750×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 9107 to 7837 computations (13.9% saved)

Pareto

0.03339063072583989

Details

analyze7.0ms (0%)

sample25.0ms (0.1%)

simplify107.0ms (0.3%)

prune7.0ms (0%)

localize10.0ms (0%)

rewrite95.0ms (0.3%)

series85.0ms (0.3%)

simplify100.0ms (0.3%)

prune522.0ms (1.7%)

localize9.0ms (0%)

rewrite100.0ms (0.3%)

series77.0ms (0.3%)

simplify82.0ms (0.3%)

prune784.0ms (2.6%)

localize11.0ms (0%)

rewrite103.0ms (0.3%)

series87.0ms (0.3%)

simplify79.0ms (0.3%)

prune1.3s (4.1%)

localize12.0ms (0%)

rewrite112.0ms (0.4%)

series90.0ms (0.3%)

simplify83.0ms (0.3%)

prune900.0ms (2.9%)

regimes2.1s (6.7%)

bsearch14.7s (47.9%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample9.1s (29.7%)

Profiling