Details

analyze315.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample48.0ms (0.3%)

Algorithm

1×

intervals

Results

26.0ms	126×	body	8192	exit
8.0ms	210×	body	128	valid
3.0ms	22×	body	512	valid
2.0ms	24×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify221.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4887	18
1	4887	18

prune7.0ms (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: 13.6b

Counts

2 → 2

Compiler

Compiled 40 to 26 computations (35% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.0b	(/.f64 x (exp.f64 wj))
5.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_3147`
48×	`add-sqr-sqrt_binary64_3169`
38×	`times-frac_binary64_3153`
23×	`add-cube-cbrt_binary64_3182`
10×	`difference-of-squares_binary64_3116`
9×	`associate-/l*_binary64_3092`
8×	`distribute-lft-out_binary64_3098`
7×	`add-cbrt-cube_binary64_3183` `associate-/r*_binary64_3091`
6×	`add-exp-log_binary64_3185`
5×	`distribute-lft-out--_binary64_3099` `add-log-exp_binary64_3186`
3×	`pow1_binary64_3208`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `associate-/l/_binary64_3094` `div-sub_binary64_3152` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `associate-/r/_binary64_3093` `div-inv_binary64_3144`
1×	`flip--_binary64_3122` `flip3--_binary64_3151` `associate-+r-_binary64_3081` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

3 → 91

Calls

3 calls:

19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
14.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))

series437.0ms (3.1%)

Counts

3 → 35

Calls

3 calls:

171.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
164.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
102.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 712 to 555 computations (22.1% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4998	2470
1	4998	2470

prune126.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	4	128

Merged error: 0.1b

Counts

128 → 4

Compiler

Compiled 2406 to 1038 computations (56.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3)))
0.0b	(-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3)))))
0.1b	(*.f64 (pow.f64 wj 3) 8/3)
8.0b	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3169`
18×	`associate-l_binary64_3088`
16×	`add-exp-log_binary64_3185`
13×	`add-cbrt-cube_binary64_3183`
12×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
11×	`pow1_binary64_3208`
9×	`add-log-exp_binary64_3186`
7×	`associate-r_binary64_3087` `prod-exp_binary64_3196`
6×	`unswap-sqr_binary64_3115` `flip-+_binary64_3121` `associate-*l/_binary64_3090` `flip3-+_binary64_3150`
5×	`cbrt-unprod_binary64_3180`
4×	`unpow-prod-down_binary64_3226` `pow-prod-down_binary64_3218` `cube-prod_binary64_3175` `frac-sub_binary64_3156`
3×	`*-commutative_binary64_3078` `cancel-sign-sub-inv_binary64_3113`
2×	`sqr-pow_binary64_3119` `diff-log_binary64_3239` `associate-*r/_binary64_3089`
1×	`pow-exp_binary64_3215` `flip--_binary64_3122` `flip3--_binary64_3151` `pow-to-exp_binary64_3216` `sub-neg_binary64_3140` `associate--r+_binary64_3083` `distribute-lft-in_binary64_3096` `cube-mult_binary64_3177` `distribute-rgt-in_binary64_3097` `unpow3_binary64_3213` `sum-log_binary64_3238`

Counts

4 → 94

Calls

4 calls:

21.0ms	(-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3)))))
14.0ms	(.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3)))
10.0ms	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))
6.0ms	(*.f64 (pow.f64 wj 3) 8/3)

series400.0ms (2.8%)

Counts

4 → 27

Calls

4 calls:

162.0ms	(-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3)))))
125.0ms	(.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3)))
75.0ms	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))
38.0ms	(*.f64 (pow.f64 wj 3) 8/3)

Compiler

Compiled 1237 to 962 computations (22.2% saved)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4987	2747
1	4987	2747

prune188.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Merged error: 0.1b

Counts

125 → 4

Compiler

Compiled 4158 to 2550 computations (38.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (exp.f64 wj))
0.0b	(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
3.9b	(-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
20.9b	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

rewrite130.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

266×	`*-un-lft-identity_binary64_3147`
213×	`add-sqr-sqrt_binary64_3169`
206×	`times-frac_binary64_3153`
76×	`add-cube-cbrt_binary64_3182`
58×	`difference-of-squares_binary64_3116`
54×	`swap-sqr_binary64_3114`
44×	`distribute-lft-out_binary64_3098`
37×	`distribute-lft-out--_binary64_3099`
30×	`associate-r_binary64_3087` `associate-l_binary64_3088`
20×	`add-cbrt-cube_binary64_3183`
19×	`add-exp-log_binary64_3185`
11×	`pow1_binary64_3208`
10×	`associate-/r/_binary64_3093`
9×	`associate-/r*_binary64_3091`
7×	`associate-/l*_binary64_3092`
6×	`cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `add-log-exp_binary64_3186` `div-inv_binary64_3144`
4×	`unswap-sqr_binary64_3115` `flip-+_binary64_3121` `flip3-+_binary64_3150` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
3×	`flip--_binary64_3122` `flip3--_binary64_3151`
2×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `associate-/l/_binary64_3094`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `cancel-sign-sub-inv_binary64_3113` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `sub-neg_binary64_3140` `div-sub_binary64_3152` `pow-plus_binary64_3210` `pow2_binary64_3228` `pow-prod-up_binary64_3217` `diff-log_binary64_3239` `associate-*r/_binary64_3089` `pow-sqr_binary64_3120`

Counts

4 → 233

Calls

4 calls:

44.0ms	(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
29.0ms	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
6.0ms	(-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
4.0ms	(/.f64 x (exp.f64 wj))

series3.0s (21.4%)

Counts

4 → 54

Calls

4 calls:

2.2s	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
423.0ms	(-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
264.0ms	(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
99.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 6944 to 4661 computations (32.9% saved)

simplify169.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4976	18191
1	4976	18191

prune695.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	287	4	291

Merged error: 0.1b

Counts

291 → 4

Compiler

Compiled 17619 to 7345 computations (58.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1)))
0.0b	(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))))
3.9b	(-.f64 (.f64 wj wj) (.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1)))))
20.6b	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

rewrite350.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

555×	`times-frac_binary64_3153`
488×	`add-sqr-sqrt_binary64_3169`
459×	`*-un-lft-identity_binary64_3147`
216×	`associate-l_binary64_3088`
195×	`add-cube-cbrt_binary64_3182`
183×	`sqrt-prod_binary64_3163`
94×	`difference-of-squares_binary64_3116`
85×	`distribute-lft-out_binary64_3098`
48×	`associate-r_binary64_3087`
47×	`distribute-lft-out--_binary64_3099`
29×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
22×	`associate-/r/_binary64_3093`
15×	`unswap-sqr_binary64_3115`
13×	`associate-/r*_binary64_3091`
11×	`cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `div-inv_binary64_3144`
10×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
9×	`associate-/l*_binary64_3092`
6×	`pow1_binary64_3208` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
4×	`flip--_binary64_3122` `flip3--_binary64_3151` `associate-/l/_binary64_3094`
2×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `div-sub_binary64_3152`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `cancel-sign-sub-inv_binary64_3113` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `sub-neg_binary64_3140` `diff-log_binary64_3239` `associate-*r/_binary64_3089`

Counts

4 → 431

Calls

4 calls:

196.0ms	(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))))
27.0ms	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
17.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1)))
6.0ms	(-.f64 (.f64 wj wj) (.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1)))))

series3.1s (22.3%)

Counts

4 → 57

Calls

4 calls:

2.2s	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
426.0ms	(-.f64 (.f64 wj wj) (.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1)))))
263.0ms	(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))))
210.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1)))

Compiler

Compiled 7219 to 4871 computations (32.5% saved)

simplify256.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5041	27198

prune1.8s (13%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	487	1	488
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	488	4	492

Merged error: 0.0b

Counts

492 → 4

Compiler

Compiled 31505 to 14212 computations (54.9% saved)

regimes236.0ms (1.7%)

Compiler: Compiled 3141 to 1851 computations (41.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	103	40
1	103	40

end0.0ms (0%)

sample2.2s (15.8%)

Algorithm

1×

intervals

Results

823.0ms	3756×	body	8192	exit
249.0ms	6535×	body	128	valid
90.0ms	702×	body	512	valid
54.0ms	736×	body	256	valid
5.0ms	27×	body	1024	valid
4.0ms	92×	body	128	invalid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 1096 to 651 computations (40.6% saved)

Details

analyze315.0ms (2.2%)

sample48.0ms (0.3%)

simplify221.0ms (1.6%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite44.0ms (0.3%)

series437.0ms (3.1%)

simplify70.0ms (0.5%)

prune126.0ms (0.9%)

localize16.0ms (0.1%)

rewrite62.0ms (0.4%)

series400.0ms (2.8%)

simplify65.0ms (0.5%)

prune188.0ms (1.3%)

localize13.0ms (0.1%)

rewrite130.0ms (0.9%)

series3.0s (21.4%)

simplify169.0ms (1.2%)

prune695.0ms (4.9%)

localize17.0ms (0.1%)

rewrite350.0ms (2.5%)

series3.1s (22.3%)

simplify256.0ms (1.8%)

prune1.8s (13%)

regimes236.0ms (1.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (15.8%)

Profiling