Details

analyze12.0ms (0.1%)

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)

sample33.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	34×	body	1024	valid
7.0ms	147×	body	128	valid
6.0ms	44×	body	512	valid
3.0ms	31×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify120.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (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

Error

9.8b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.6b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
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))
2.6b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite121.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_2465`
74×	`times-frac_binary64_2471`
72×	`add-sqr-sqrt_binary64_2487`
39×	`add-cube-cbrt_binary64_2500`
26×	`cancel-sign-sub-inv_binary64_2431`
18×	`distribute-lft-out--_binary64_2417`
17×	`distribute-lft-out_binary64_2416`
14×	`difference-of-squares_binary64_2434` `associate-+l+_binary64_2398`
12×	`add-exp-log_binary64_2503`
11×	`add-log-exp_binary64_2504` `associate-/r*_binary64_2409`
10×	`div-inv_binary64_2462`
8×	`add-cbrt-cube_binary64_2501`
6×	`pow1_binary64_2526` `associate-/l*_binary64_2410`
4×	`difference-of-sqr-1_binary64_2435` `div-exp_binary64_2516` `associate-/r/_binary64_2411`
3×	`flip--_binary64_2440` `flip3--_binary64_2469` `frac-add_binary64_2473`
2×	`flip3-+_binary64_2468` `sum-log_binary64_2556` `inv-pow_binary64_2550` `pow-flip_binary64_2539` `flip-+_binary64_2439` `rec-exp_binary64_2515` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `1-exp_binary64_2509` `frac-sub_binary64_2474`
1×	`associate-+l-_binary64_2400` `+-commutative_binary64_2395`

Counts

4 → 161

Calls

8 calls:

53.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
29.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
10.0ms	(/.f64 1 (+.f64 x 1))
10.0ms	(/.f64 1 (-.f64 x 1))
0.0ms	(/.f64 1 (-.f64 x 1))

series311.0ms (2.8%)

Counts

4 → 47

Calls

4 calls:

144.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
58.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
55.0ms	(/.f64 1 (+.f64 x 1))
53.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 880 to 759 computations (13.8% saved)

simplify157.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4938	3281
1	4938	3281

prune408.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	206	3	209

Error

0.3b

Counts

209 → 3

Compiler

Compiled 4172 to 3314 computations (20.6% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x))
0.1b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
6.5b	(+.f64 (-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite573.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

459×	`times-frac_binary64_2471`
363×	`*-un-lft-identity_binary64_2465`
285×	`add-sqr-sqrt_binary64_2487`
242×	`sqrt-prod_binary64_2481`
202×	`add-cube-cbrt_binary64_2500`
64×	`distribute-lft-out_binary64_2416`
30×	`associate-/l*_binary64_2410`
26×	`cancel-sign-sub-inv_binary64_2431`
22×	`difference-of-squares_binary64_2434`
20×	`associate-/r/_binary64_2411` `sqrt-div_binary64_2482`
17×	`add-exp-log_binary64_2503` `div-inv_binary64_2462`
14×	`associate-/r*_binary64_2409` `associate-+l+_binary64_2398`
11×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `flip-+_binary64_2439` `distribute-lft-out--_binary64_2417` `add-cbrt-cube_binary64_2501`
8×	`div-exp_binary64_2516`
6×	`pow1_binary64_2526`
4×	`cbrt-undiv_binary64_2499`
3×	`pow-flip_binary64_2539` `frac-add_binary64_2473`
2×	`flip--_binary64_2440` `sum-log_binary64_2556` `rec-exp_binary64_2515` `clear-num_binary64_2464` `sub-neg_binary64_2458` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `flip3--_binary64_2469` `1-exp_binary64_2509` `frac-sub_binary64_2474`
1×	`associate-+l-_binary64_2400` `+-commutative_binary64_2395` `inv-pow_binary64_2550` `pow1/2_binary64_2545` `associate-/l/_binary64_2412` `sqrt-pow1_binary64_2483`

Counts

4 → 381

Calls

8 calls:

244.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
220.0ms	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x))
26.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.0ms	(/.f64 1 (-.f64 x 1))

series237.0ms (2.2%)

Counts

4 → 41

Calls

4 calls:

129.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
44.0ms	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1))) (/.f64 2 x))
35.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 x 1)))
29.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 835 to 718 computations (14% saved)

simplify250.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4987	10125
1	4987	10125

prune1.3s (11.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	422	3	425

Error

0.3b

Counts

425 → 3

Compiler

Compiled 11506 to 9496 computations (17.5% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(-.f64 (pow.f64 x 3) x)
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
15.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite88.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_2487`
42×	`associate-*r/_binary64_2407`
34×	`*-un-lft-identity_binary64_2465`
32×	`frac-add_binary64_2473`
27×	`times-frac_binary64_2471`
26×	`flip--_binary64_2440` `flip3--_binary64_2469`
20×	`add-cube-cbrt_binary64_2500`
19×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
18×	`associate-/l/_binary64_2412`
16×	`difference-of-squares_binary64_2434` `frac-times_binary64_2475`
9×	`associate-/r*_binary64_2409`
8×	`associate-*l/_binary64_2408` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`pow1_binary64_2526`
4×	`distribute-lft-in_binary64_2414` `unpow3_binary64_2531` `associate-+l+_binary64_2398` `cube-prod_binary64_2493` `distribute-lft-out--_binary64_2417` `distribute-rgt-in_binary64_2415` `unpow-prod-down_binary64_2544` `sqr-pow_binary64_2437` `associate-r_binary64_2405` `distribute-rgt-out--_binary64_2419`
3×	`sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `associate-/l_binary64_2410` `associate-l*_binary64_2406`
2×	`associate-+r+_binary64_2397` `associate-/r/_binary64_2411`
1×	`*-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416` `cbrt-unprod_binary64_2498`

Counts

4 → 139

Calls

8 calls:

32.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
17.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
11.0ms	(*.f64 x (+.f64 1 x))
6.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))

series182.0ms (1.6%)

Counts

4 → 26

Calls

4 calls:

76.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
46.0ms	(*.f64 x (+.f64 1 x))
41.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
19.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

Compiler

Compiled 615 to 496 computations (19.3% saved)

simplify134.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	6051	6218

prune422.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	165	3	168

Error

0.3b

Counts

168 → 3

Compiler

Compiled 6616 to 4616 computations (30.2% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 2 (pow.f64 x 3))
0.3b	(/.f64 2 (pow.f64 x 3))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_2471`
26×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
12×	`associate-/r*_binary64_2409` `cube-prod_binary64_2493` `unpow-prod-down_binary64_2544`
6×	`add-exp-log_binary64_2503`
4×	`unpow3_binary64_2531` `cube-mult_binary64_2495` `sqr-pow_binary64_2437`
3×	`add-cbrt-cube_binary64_2501` `div-exp_binary64_2516` `associate-/l*_binary64_2410`
1×	`add-log-exp_binary64_2504` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `div-inv_binary64_2462` `pow1_binary64_2526` `frac-2neg_binary64_2476`

Counts

1 → 65

Calls

2 calls:

5.0ms	(/.f64 2 (pow.f64 x 3))
0.0ms	(/.f64 2 (pow.f64 x 3))

series43.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

43.0ms

(/.f64 2 (pow.f64 x 3))

Compiler

Compiled 30 to 30 computations (0% saved)

simplify104.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4950	839
1	4950	839

prune102.0ms (0.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Error

Counts

71 → 7

Compiler

Compiled 692 to 504 computations (27.2% saved)

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	348	1441
1	348	1441

regimes163.0ms (1.5%)

Accuracy

Total 0.1b remaining (97.7%)

Threshold costs 0.1b (97.7%)

Compiler

Compiled 962 to 808 computations (16% saved)

bsearch59.0ms (0.5%)

Steps

Iters	Range		Point
10	15.314453761328926	18382883363495.402	85378974.07205185
9	-36601195461283.35	-30245.619272263048	-137437521.367165

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	66
1	70	66

end0.0ms (0%)

sample6.1s (55.4%)

Algorithm

1×

intervals

Results

239.0ms	1269×	body	1024	valid
224.0ms	4477×	body	128	valid
222.0ms	1514×	body	512	valid
70.0ms	740×	body	256	valid

Compiler

Compiled 2995 to 2502 computations (16.5% saved)

Pareto

-0.07293308558849797

Details

analyze12.0ms (0.1%)

sample33.0ms (0.3%)

simplify120.0ms (1.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite121.0ms (1.1%)

series311.0ms (2.8%)

simplify157.0ms (1.4%)

prune408.0ms (3.7%)

localize17.0ms (0.2%)

rewrite573.0ms (5.2%)

series237.0ms (2.2%)

simplify250.0ms (2.3%)

prune1.3s (11.7%)

localize13.0ms (0.1%)

rewrite88.0ms (0.8%)

series182.0ms (1.6%)

simplify134.0ms (1.2%)

prune422.0ms (3.8%)

localize6.0ms (0%)

rewrite10.0ms (0.1%)

series43.0ms (0.4%)

simplify104.0ms (0.9%)

prune102.0ms (0.9%)

simplify38.0ms (0.3%)

regimes163.0ms (1.5%)

bsearch59.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (55.4%)

Profiling