Details

analyze334.0ms (3.5%)

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)

sample54.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	121×	body	8192	exit
8.0ms	209×	body	128	valid
4.0ms	26×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify239.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4887	18
1	4887	18

prune5.0ms (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

Error

13.5b

Counts

2 → 2

Compiler

Compiled 40 to 26 computations (35% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

4.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_3068`
48×	`add-sqr-sqrt_binary64_3090`
38×	`times-frac_binary64_3074`
23×	`add-cube-cbrt_binary64_3103`
10×	`difference-of-squares_binary64_3037`
9×	`associate-/l*_binary64_3013`
8×	`distribute-lft-out_binary64_3019`
7×	`add-cbrt-cube_binary64_3104` `associate-/r*_binary64_3012`
6×	`add-exp-log_binary64_3106`
5×	`distribute-lft-out--_binary64_3020` `add-log-exp_binary64_3107`
3×	`pow1_binary64_3129`
2×	`flip3-+_binary64_3071` `associate-/r/_binary64_3014` `div-inv_binary64_3065` `cbrt-undiv_binary64_3102` `frac-2neg_binary64_3079` `div-exp_binary64_3119` `div-sub_binary64_3073` `associate-/l/_binary64_3015` `flip-+_binary64_3042` `clear-num_binary64_3067`
1×	`associate-+r-_binary64_3002` `sum-log_binary64_3159` `flip--_binary64_3043` `+-commutative_binary64_2998` `flip3--_binary64_3072`

Counts

3 → 91

Calls

6 calls:

19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))
0.0ms	(/.f64 x (exp.f64 wj))
0.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

series390.0ms (4%)

Counts

3 → 45

Calls

3 calls:

165.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
155.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
69.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 846 to 635 computations (24.9% saved)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4955	2769
1	4955	2769

prune166.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	4	138

Error

0.1b

Counts

138 → 4

Compiler

Compiled 2611 to 1090 computations (58.3% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3))))
0.0b	(+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3))
0.0b	(+.f64 (*.f64 5/2 x) 1)
0.0b	(+.f64 x (-.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))))))
0.0b	(.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)))))
0.2b	(*.f64 (pow.f64 wj 3) 8/3)
5.6b	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3090`
18×	`associate-l_binary64_3009`
16×	`add-exp-log_binary64_3106`
13×	`add-cbrt-cube_binary64_3104`
12×	`add-cube-cbrt_binary64_3103` `*-un-lft-identity_binary64_3068`
11×	`pow1_binary64_3129`
9×	`add-log-exp_binary64_3107`
7×	`prod-exp_binary64_3117` `associate-r_binary64_3008`
6×	`flip3-+_binary64_3071` `associate-*l/_binary64_3011` `flip-+_binary64_3042` `unswap-sqr_binary64_3036`
5×	`cbrt-unprod_binary64_3101`
4×	`cube-prod_binary64_3096` `unpow-prod-down_binary64_3147` `frac-sub_binary64_3077` `pow-prod-down_binary64_3139`
3×	`*-commutative_binary64_2999` `cancel-sign-sub-inv_binary64_3034`
2×	`diff-log_binary64_3160` `associate-*r/_binary64_3010` `sqr-pow_binary64_3040`
1×	`associate--r+_binary64_3004` `pow-to-exp_binary64_3137` `sub-neg_binary64_3061` `sum-log_binary64_3159` `flip--_binary64_3043` `flip3--_binary64_3072` `cube-mult_binary64_3098` `distribute-lft-in_binary64_3017` `pow-exp_binary64_3136` `unpow3_binary64_3134` `distribute-rgt-in_binary64_3018`

Counts

4 → 94

Calls

8 calls:

22.0ms	(-.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)))))
11.0ms	(.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))
7.0ms	(*.f64 (pow.f64 wj 3) 8/3)
0.0ms	(+.f64 x (-.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))))))

series702.0ms (7.3%)

Counts

4 → 36

Calls

4 calls:

386.0ms	(-.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)))))
168.0ms	(.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3)))
114.0ms	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))
33.0ms	(*.f64 (pow.f64 wj 3) 8/3)

Compiler

Compiled 1495 to 1157 computations (22.6% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4966	2961
1	4966	2961

prune229.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	128	6	134

Error

0.1b

Counts

134 → 6

Compiler

Compiled 4477 to 2763 computations (38.3% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (*.f64 wj wj) 1))
0.0b	(-.f64 (*.f64 wj wj) 1)
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (*.f64 wj wj) 1))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1))
4.4b	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1)))

rewrite79.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`add-sqr-sqrt_binary64_3090`
95×	`times-frac_binary64_3074`
86×	`*-un-lft-identity_binary64_3068`
54×	`difference-of-squares_binary64_3037`
44×	`add-cube-cbrt_binary64_3103`
42×	`associate-l_binary64_3009`
14×	`distribute-lft-out--_binary64_3020` `difference-of-sqr-1_binary64_3038`
13×	`add-cbrt-cube_binary64_3104`
12×	`add-exp-log_binary64_3106` `cancel-sign-sub-inv_binary64_3034`
9×	`associate-/l_binary64_3013` `associate-/r_binary64_3012`
8×	`associate-+r+_binary64_3000` `distribute-lft-in_binary64_3017` `distribute-rgt-in_binary64_3018`
7×	`associate-r_binary64_3008`
6×	`pow1_binary64_3129` `add-log-exp_binary64_3107`
5×	`flip--_binary64_3043` `flip3--_binary64_3072`
4×	`sub-neg_binary64_3061` `associate-/r/_binary64_3014`
3×	`div-inv_binary64_3065` `cbrt-undiv_binary64_3102` `div-exp_binary64_3119`
2×	`prod-exp_binary64_3117` `cbrt-unprod_binary64_3101` `frac-times_binary64_3078` `associate-*r/_binary64_3010` `frac-2neg_binary64_3079` `associate-/l/_binary64_3015` `clear-num_binary64_3067` `unswap-sqr_binary64_3036`
1×	`flip3-+_binary64_3071` `sum-log_binary64_3159` `associate-l/_binary64_3011` `+-commutative_binary64_2998` `-commutative_binary64_2999` `div-sub_binary64_3073` `flip-+_binary64_3042` `pow-prod-down_binary64_3139`

Counts

4 → 188

Calls

8 calls:

27.0ms	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1))
19.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (*.f64 wj wj) 1))
6.0ms	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1)))
4.0ms	(/.f64 x (exp.f64 wj))
0.0ms	(-.f64 (*.f64 wj wj) 1)

series931.0ms (9.7%)

Counts

4 → 59

Calls

4 calls:

450.0ms	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1)))
252.0ms	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (.f64 wj wj) 1)) (-.f64 wj 1))
164.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (*.f64 wj wj) 1))
65.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 1691 to 1265 computations (25.2% saved)

simplify118.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5490	5734

prune252.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	247	6	253

Error

0.1b

Counts

253 → 6

Compiler

Compiled 6272 to 2633 computations (58% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 1 (+.f64 wj 1))
0.0b	(*.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1)))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 1 (+.f64 wj 1))
0.0b	(.f64 (.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))) (-.f64 wj 1))
4.4b	(+.f64 wj (.f64 (.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))) (-.f64 wj 1)))

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log_binary64_3106`
37×	`*-un-lft-identity_binary64_3068`
30×	`add-sqr-sqrt_binary64_3090`
26×	`add-cbrt-cube_binary64_3104` `add-cube-cbrt_binary64_3103`
21×	`times-frac_binary64_3074`
17×	`prod-exp_binary64_3117`
12×	`cancel-sign-sub-inv_binary64_3034`
11×	`div-exp_binary64_3119`
10×	`pow1_binary64_3129`
9×	`cbrt-unprod_binary64_3101` `frac-times_binary64_3078`
8×	`associate-+r+_binary64_3000` `distribute-lft-in_binary64_3017` `distribute-rgt-in_binary64_3018`
7×	`associate-r_binary64_3008` `associate-/r*_binary64_3012`
6×	`associate-/l_binary64_3013` `associate-l/_binary64_3011` `cbrt-undiv_binary64_3102` `add-log-exp_binary64_3107`
5×	`associate-*r/_binary64_3010`
4×	`sub-neg_binary64_3061` `distribute-lft-out_binary64_3019` `flip--_binary64_3043` `flip3--_binary64_3072`
3×	`rec-exp_binary64_3118` `1-exp_binary64_3112` `pow-prod-down_binary64_3139`
2×	`flip3-+_binary64_3071` `difference-of-squares_binary64_3037` `associate-/r/_binary64_3014` `div-inv_binary64_3065` `frac-2neg_binary64_3079` `flip-+_binary64_3042` `clear-num_binary64_3067`
1×	`distribute-lft-out--_binary64_3020` `pow-flip_binary64_3142` `sum-log_binary64_3159` `+-commutative_binary64_2998` `inv-pow_binary64_3153` `difference-of-sqr-1_binary64_3038` `-commutative_binary64_2999` `associate-l*_binary64_3009`

Counts

4 → 134

Calls

8 calls:

32.0ms	(.f64 (.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))) (-.f64 wj 1))
7.0ms	(+.f64 wj (.f64 (.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))) (-.f64 wj 1)))
5.0ms	(/.f64 1 (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))
0.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))

series438.0ms (4.5%)

Counts

4 → 57

Calls

4 calls:

174.0ms	(+.f64 wj (.f64 (.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))) (-.f64 wj 1)))
154.0ms	(.f64 (.f64 (/.f64 1 (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 wj 1))) (-.f64 wj 1))
74.0ms	(/.f64 x (exp.f64 wj))
36.0ms	(/.f64 1 (+.f64 wj 1))

Compiler

Compiled 1308 to 995 computations (23.9% saved)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5079	3406

prune200.0ms (2.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	191	6	197

Error

0.1b

Counts

197 → 6

Compiler

Compiled 4458 to 2306 computations (48.3% saved)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	2304	1408
1	2304	1408

regimes302.0ms (3.1%)

Accuracy

Total 0.6b remaining (86.6%)

Threshold costs 0.6b (86.6%)

Compiler

Compiled 2850 to 1863 computations (34.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 16 to 8 computations (50% saved)

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	712	103
1	712	103

end0.0ms (0%)

sample4.6s (47.6%)

Algorithm

1×

intervals

Results

941.0ms	3863×	body	8192	exit
258.0ms	6533×	body	128	valid
85.0ms	690×	body	512	valid
62.0ms	741×	body	256	valid
7.0ms	36×	body	1024	valid
3.0ms	70×	body	128	invalid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 2933 to 1914 computations (34.7% saved)

Pareto

0.19192315656141953

Details

analyze334.0ms (3.5%)

sample54.0ms (0.6%)

simplify239.0ms (2.5%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite45.0ms (0.5%)

series390.0ms (4%)

simplify89.0ms (0.9%)

prune166.0ms (1.7%)

localize18.0ms (0.2%)

rewrite61.0ms (0.6%)

series702.0ms (7.3%)

simplify92.0ms (0.9%)

prune229.0ms (2.4%)

localize12.0ms (0.1%)

rewrite79.0ms (0.8%)

series931.0ms (9.7%)

simplify118.0ms (1.2%)

prune252.0ms (2.6%)

localize13.0ms (0.1%)

rewrite64.0ms (0.7%)

series438.0ms (4.5%)

simplify89.0ms (0.9%)

prune200.0ms (2.1%)

simplify97.0ms (1%)

regimes302.0ms (3.1%)

bsearch3.0ms (0%)

simplify25.0ms (0.3%)

end0.0ms (0%)

sample4.6s (47.6%)

Profiling