Details

analyze12.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample36.0ms (0%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify228.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5047	13

prune15.0ms (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: 0.6b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
0.4b	(/.f64 1 (*.f64 i i))
0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_3169`
40×	`times-frac_binary64_3153` `*-un-lft-identity_binary64_3147`
20×	`add-cube-cbrt_binary64_3182`
16×	`add-exp-log_binary64_3185`
15×	`difference-of-squares_binary64_3116`
11×	`pow1_binary64_3208`
10×	`add-cbrt-cube_binary64_3183` `distribute-lft-out--_binary64_3099`
9×	`associate-/r*_binary64_3091`
8×	`div-inv_binary64_3144`
7×	`cancel-sign-sub-inv_binary64_3113`
6×	`pow-flip_binary64_3221` `associate-/l*_binary64_3092`
5×	`div-exp_binary64_3198` `add-log-exp_binary64_3186`
3×	`prod-exp_binary64_3196` `cbrt-undiv_binary64_3181`
2×	`flip--_binary64_3122` `clear-num_binary64_3146` `flip3--_binary64_3151` `frac-2neg_binary64_3158` `associate-/r/_binary64_3093` `1-exp_binary64_3191` `rec-exp_binary64_3197`
1×	`pow-prod-down_binary64_3218` `inv-pow_binary64_3232` `sub-neg_binary64_3140` `pow-plus_binary64_3210` `pow2_binary64_3228` `pow-prod-up_binary64_3217` `cbrt-unprod_binary64_3180` `diff-log_binary64_3239` `pow-sqr_binary64_3120`

Counts

3 → 104

Calls

3 calls:

14.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
11.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
9.0ms	(/.f64 1 (*.f64 i i))

series79.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

30.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
29.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
19.0ms	(/.f64 1 (*.f64 i i))

simplify121.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5121	1524

prune1.1s (1.2%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	82	31	113
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	82	33	115

Merged error: 0b

Counts

115 → 33

Compiler

Compiled 2124 to 1657 computations (22% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 2 (fabs.f64 (/.f64 1 i)))
0.0b	(*.f64 (/.f64 1 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
0.1b	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
0.1b	(/.f64 1 (+.f64 2 (fabs.f64 (/.f64 1 i))))

rewrite98.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-sqr-sqrt_binary64_3169`
73×	`*-un-lft-identity_binary64_3147`
61×	`times-frac_binary64_3153`
41×	`add-cube-cbrt_binary64_3182`
32×	`add-exp-log_binary64_3185`
21×	`associate-r_binary64_3087`
20×	`add-cbrt-cube_binary64_3183`
18×	`associate-l_binary64_3088`
11×	`div-exp_binary64_3198`
9×	`associate-/r*_binary64_3091`
8×	`distribute-lft-out--_binary64_3099` `prod-exp_binary64_3196` `difference-of-squares_binary64_3116` `associate-/r/_binary64_3093`
7×	`distribute-lft-out_binary64_3098` `pow1_binary64_3208`
6×	`unswap-sqr_binary64_3115` `cbrt-undiv_binary64_3181` `add-log-exp_binary64_3186` `associate-/l*_binary64_3092`
4×	`cbrt-unprod_binary64_3180` `div-inv_binary64_3144`
3×	`flip--_binary64_3122` `cancel-sign-sub-inv_binary64_3113` `flip3--_binary64_3151` `1-exp_binary64_3191` `rec-exp_binary64_3197`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `inv-pow_binary64_3232` `sub-neg_binary64_3140` `pow-flip_binary64_3221` `diff-log_binary64_3239` `associate-*r/_binary64_3089`

Counts

4 → 159

Calls

4 calls:

37.0ms	(*.f64 (/.f64 1 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
15.0ms	(/.f64 1 (+.f64 2 (fabs.f64 (/.f64 1 i))))
10.0ms	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
7.0ms	(-.f64 2 (fabs.f64 (/.f64 1 i)))

series341.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(*.f64 (/.f64 1 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
73.0ms	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
54.0ms	(/.f64 1 (+.f64 2 (fabs.f64 (/.f64 1 i))))
37.0ms	(-.f64 2 (fabs.f64 (/.f64 1 i)))

simplify418.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (273.0ms)

Iter	Nodes	Cost
0	5539	3603

prune3.4s (3.8%)

Pruning

84 alts after pruning (82 fresh and 2 done)

	Pruned	Kept	Total
New	113	58	171
Fresh	7	24	31
Picked	0	1	1
Done	0	1	1
Total	120	84	204

Merged error: 0b

Counts

204 → 84

Compiler

Compiled 6265 to 5612 computations (10.4% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 2 (fabs.f64 (/.f64 1 i)))
0.0b	(.f64 (.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 1) (+.f64 2 (fabs.f64 (/.f64 1 i))))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
0.1b	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
0.1b	(/.f64 (cbrt.f64 1) (+.f64 2 (fabs.f64 (/.f64 1 i))))

rewrite115.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_3147`
54×	`times-frac_binary64_3153` `add-sqr-sqrt_binary64_3169`
49×	`add-exp-log_binary64_3185`
40×	`add-cube-cbrt_binary64_3182`
36×	`add-cbrt-cube_binary64_3183`
22×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
21×	`associate-r_binary64_3087`
15×	`cbrt-prod_binary64_3178`
13×	`pow1_binary64_3208`
11×	`cbrt-undiv_binary64_3181` `div-exp_binary64_3198`
9×	`associate-/r_binary64_3091` `associate-/l_binary64_3092`
8×	`distribute-lft-out_binary64_3098`
7×	`distribute-lft-out--_binary64_3099` `difference-of-squares_binary64_3116`
6×	`pow-prod-down_binary64_3218` `add-log-exp_binary64_3186` `associate-/r/_binary64_3093`
3×	`associate-*r/_binary64_3089` `div-inv_binary64_3144`
2×	`flip--_binary64_3122` `clear-num_binary64_3146` `flip-+_binary64_3121` `flip3--_binary64_3151` `frac-2neg_binary64_3158` `flip3-+_binary64_3150`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `associate-l/_binary64_3090` `+-commutative_binary64_3077` `associate-l_binary64_3088` `sum-log_binary64_3238`

Counts

4 → 153

Calls

4 calls:

47.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 1) (+.f64 2 (fabs.f64 (/.f64 1 i))))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
13.0ms	(/.f64 (cbrt.f64 1) (+.f64 2 (fabs.f64 (/.f64 1 i))))
11.0ms	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
7.0ms	(+.f64 2 (fabs.f64 (/.f64 1 i)))

series321.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 1) (+.f64 2 (fabs.f64 (/.f64 1 i))))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
99.0ms	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
54.0ms	(/.f64 (cbrt.f64 1) (+.f64 2 (fabs.f64 (/.f64 1 i))))
11.0ms	(+.f64 2 (fabs.f64 (/.f64 1 i)))

simplify247.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4951	3558
1	4951	3558

prune5.5s (6.1%)

Pruning

112 alts after pruning (109 fresh and 3 done)

	Pruned	Kept	Total
New	129	36	165
Fresh	8	73	81
Picked	0	1	1
Done	0	2	2
Total	137	112	249

Merged error: 0b

Counts

249 → 112

Compiler

Compiled 7888 to 7206 computations (8.6% saved)

localize64.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 2 (fabs.f64 (/.f64 1 i)))
0.0b	(.f64 (.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 (sqrt.f64 1)) (/.f64 (+.f64 2 (fabs.f64 (/.f64 1 i))) (cbrt.f64 1)))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
0.1b	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
0.1b	(/.f64 (cbrt.f64 (sqrt.f64 1)) (/.f64 (+.f64 2 (fabs.f64 (/.f64 1 i))) (cbrt.f64 1)))

rewrite568.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64_3153`
396×	`*-un-lft-identity_binary64_3147`
294×	`cbrt-prod_binary64_3178`
274×	`add-sqr-sqrt_binary64_3169`
260×	`add-cube-cbrt_binary64_3182`
87×	`sqrt-prod_binary64_3163`
76×	`add-exp-log_binary64_3185`
61×	`distribute-lft-out_binary64_3098`
49×	`add-cbrt-cube_binary64_3183`
33×	`associate-/r*_binary64_3091`
32×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
23×	`cbrt-undiv_binary64_3181` `div-exp_binary64_3198`
21×	`associate-r_binary64_3087`
13×	`pow1_binary64_3208` `div-inv_binary64_3144`
12×	`associate-/l*_binary64_3092`
7×	`distribute-lft-out--_binary64_3099` `difference-of-squares_binary64_3116`
6×	`pow-prod-down_binary64_3218` `add-log-exp_binary64_3186`
5×	`associate-/r/_binary64_3093`
3×	`associate-*r/_binary64_3089`
2×	`flip--_binary64_3122` `clear-num_binary64_3146` `flip3--_binary64_3151` `frac-2neg_binary64_3158`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `flip-+_binary64_3121` `associate-l/_binary64_3090` `flip3-+_binary64_3150` `+-commutative_binary64_3077` `associate-l_binary64_3088` `sum-log_binary64_3238`

Counts

4 → 417

Calls

4 calls:

200.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 (sqrt.f64 1)) (/.f64 (+.f64 2 (fabs.f64 (/.f64 1 i))) (cbrt.f64 1)))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
72.0ms	(/.f64 (cbrt.f64 (sqrt.f64 1)) (/.f64 (+.f64 2 (fabs.f64 (/.f64 1 i))) (cbrt.f64 1)))
24.0ms	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
12.0ms	(+.f64 2 (fabs.f64 (/.f64 1 i)))

series636.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

318.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 (sqrt.f64 1)) (/.f64 (+.f64 2 (fabs.f64 (/.f64 1 i))) (cbrt.f64 1)))) (/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
152.0ms	(/.f64 1/4 (-.f64 2 (fabs.f64 (/.f64 1 i))))
150.0ms	(/.f64 (cbrt.f64 (sqrt.f64 1)) (/.f64 (+.f64 2 (fabs.f64 (/.f64 1 i))) (cbrt.f64 1)))
16.0ms	(+.f64 2 (fabs.f64 (/.f64 1 i)))

simplify613.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

429 → 429

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4920	14210
1	4920	14210

prune18.0s (20%)

Pruning

163 alts after pruning (159 fresh and 4 done)

	Pruned	Kept	Total
New	347	82	429
Fresh	31	77	108
Picked	0	1	1
Done	0	3	3
Total	378	163	541

Merged error: 0b

Counts

541 → 163

Compiler

Compiled 15738 to 14611 computations (7.2% saved)

regimes6.2s (6.9%)

Compiler: Compiled 27224 to 25562 computations (6.1% saved)

bsearch3.8s (4.3%)

simplify20.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	57
1	34	57

end0.0ms (0%)

sample47.7s (53.2%)

Algorithm

1×

intervals

Results

870.0ms	8000×	body	128	valid
205.0ms	8000×	pre	128	true

Compiler

Compiled 13925 to 13078 computations (6.1% saved)

Pareto

0.4615384615384615

Details

analyze12.0ms (0%)

sample36.0ms (0%)

simplify228.0ms (0.3%)

prune15.0ms (0%)

localize11.0ms (0%)

rewrite46.0ms (0.1%)

series79.0ms (0.1%)

simplify121.0ms (0.1%)

prune1.1s (1.2%)

localize18.0ms (0%)

rewrite98.0ms (0.1%)

series341.0ms (0.4%)

simplify418.0ms (0.5%)

prune3.4s (3.8%)

localize27.0ms (0%)

rewrite115.0ms (0.1%)

series321.0ms (0.4%)

simplify247.0ms (0.3%)

prune5.5s (6.1%)

localize64.0ms (0.1%)

rewrite568.0ms (0.6%)

series636.0ms (0.7%)

simplify613.0ms (0.7%)

prune18.0s (20%)

regimes6.2s (6.9%)

bsearch3.8s (4.3%)

simplify20.0ms (0%)

end0.0ms (0%)

sample47.7s (53.2%)

Profiling