Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample25.0ms (0%)

Algorithm

1×

intervals

Results

6.0ms	194×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	29×	body	1024	valid
2.0ms	22×	body	512	valid
1.0ms	4×	body	2048	valid
0.0ms	7×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify344.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (246.0ms)

Iter	Nodes	Cost
0	5018	19

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

Error

15.5b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.6b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2465`
26×	`add-sqr-sqrt_binary64_2487`
25×	`times-frac_binary64_2471`
19×	`distribute-lft-out_binary64_2416`
14×	`add-cube-cbrt_binary64_2500`
6×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
5×	`associate-/r_binary64_2409` `associate-/l_binary64_2410`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
2×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `div-sub_binary64_2470` `pow1_binary64_2526` `associate-/r/_binary64_2411`
1×	`associate-+l-_binary64_2400` `+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `flip3--_binary64_2469`

Counts

2 → 65

Calls

2 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series382.0ms (0.5%)

Counts

2 → 44

Calls

2 calls:

237.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
146.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1994 to 1666 computations (16.4% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4957	3204
1	4957	3204

prune151.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

0.0b

Counts

110 → 5

Compiler

Compiled 2889 to 1696 computations (41.3% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 beta alpha) 2))
0.1b	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2)))
3.8b	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2))) 1)

rewrite49.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64_2465`
32×	`times-frac_binary64_2471` `add-sqr-sqrt_binary64_2487`
23×	`add-cube-cbrt_binary64_2500`
21×	`associate-r_binary64_2405` `distribute-lft-out_binary64_2416`
16×	`add-exp-log_binary64_2503`
10×	`add-cbrt-cube_binary64_2501`
6×	`pow1_binary64_2526`
5×	`add-log-exp_binary64_2504` `associate-/r_binary64_2409` `associate-l*_binary64_2406`
4×	`div-exp_binary64_2516` `associate-/r/_binary64_2411` `prod-exp_binary64_2514`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `associate-/l*_binary64_2410`
2×	`associate-*l/_binary64_2408` `frac-times_binary64_2475` `flip--_binary64_2440` `rec-exp_binary64_2515` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `flip3--_binary64_2469` `1-exp_binary64_2509` `cbrt-unprod_binary64_2498`
1×	`difference-of-squares_binary64_2434` `-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `inv-pow_binary64_2550` `pow-flip_binary64_2539` `associate-r/_binary64_2407` `clear-num_binary64_2464` `distribute-lft-out--_binary64_2417` `un-div-inv_binary64_2463` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536`

Counts

3 → 102

Calls

3 calls:

18.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2)))
14.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2))) 1)
8.0ms	(/.f64 1 (+.f64 (+.f64 beta alpha) 2))

series510.0ms (0.7%)

Counts

3 → 66

Calls

3 calls:

238.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2))) 1)
147.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2)))
124.0ms	(/.f64 1 (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 2898 to 2412 computations (16.8% saved)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5296	4341

prune396.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	168	5	173

Error

0.0b

Counts

173 → 5

Compiler

Compiled 4406 to 2700 computations (38.7% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)) (+.f64 1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) (-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))))
0.1b	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)
1.6b	(+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3))
1.8b	(-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite122.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`*-un-lft-identity_binary64_2465`
68×	`add-sqr-sqrt_binary64_2487`
65×	`times-frac_binary64_2471`
37×	`add-cube-cbrt_binary64_2500`
35×	`distribute-lft-out_binary64_2416`
31×	`cube-prod_binary64_2493` `unpow-prod-down_binary64_2544`
14×	`difference-of-squares_binary64_2434`
11×	`distribute-lft-out--_binary64_2417`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504`
6×	`associate-/r/_binary64_2411`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `pow1_binary64_2526`
4×	`associate-/l*_binary64_2410`
3×	`associate-/r*_binary64_2409` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `pow-unpow_binary64_2542`
2×	`rem-cube-cbrt_binary64_2488` `difference-of-sqr-1_binary64_2435` `associate-/l/_binary64_2412` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `div-exp_binary64_2516`
1×	`unpow3_binary64_2531` `+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate--l-_binary64_2403` `clear-num_binary64_2464` `div-sub_binary64_2470` `sub-neg_binary64_2458` `cube-mult_binary64_2495` `pow-to-exp_binary64_2534` `sqr-pow_binary64_2437` `diff-log_binary64_2557` `pow-pow_binary64_2537` `frac-2neg_binary64_2476` `cube-div_binary64_2494` `flip3--_binary64_2469`

Counts

4 → 151

Calls

4 calls:

32.0ms	(/.f64 (+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)) (+.f64 1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) (-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))))
32.0ms	(+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3))
22.0ms	(-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
15.0ms	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)

series1.1min (88.1%)

Counts

4 → 74

Calls

4 calls:

1.0min	(/.f64 (+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)) (+.f64 1 (*.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) (-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))))
506.0ms	(+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3))
229.0ms	(-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
201.0ms	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)

Compiler

Compiled 36628 to 29069 computations (20.6% saved)

simplify370.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5296	56319

prune4.1s (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	225	5	230

Error

0.0b

Counts

230 → 5

Compiler

Compiled 43148 to 28895 computations (33% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 2 (*.f64 beta 2)) alpha)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_2465` `times-frac_binary64_2471`
11×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
5×	`associate-/l*_binary64_2410`
4×	`distribute-rgt1-in_binary64_2421` `distribute-rgt-out_binary64_2418`
3×	`associate-/r*_binary64_2409` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
2×	`associate-/l/_binary64_2412`
1×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `pow1_binary64_2526` `frac-2neg_binary64_2476`

Counts

1 → 37

Calls

1 calls:

5.0ms

(/.f64 (+.f64 2 (*.f64 beta 2)) alpha)

series84.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

84.0ms

(/.f64 (+.f64 2 (*.f64 beta 2)) alpha)

Compiler

Compiled 151 to 146 computations (3.3% saved)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	6271	668

prune36.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	46	5	51

Error

0.0b

Counts

51 → 5

Compiler

Compiled 648 to 485 computations (25.2% saved)

regimes319.0ms (0.4%)

Accuracy

Total 0.0b remaining (58.4%)

Threshold costs 0.0b (58.4%)

Compiler

Compiled 3734 to 2789 computations (25.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	92
1	90	92

end0.0ms (0%)

sample1.4s (1.9%)

Algorithm

1×

intervals

Results

204.0ms	5965×	body	128	valid
149.0ms	8000×	pre	128	true
130.0ms	1016×	body	1024	valid
59.0ms	597×	body	512	valid
20.0ms	306×	body	256	valid
18.0ms	116×	body	2048	valid

Compiler

Compiled 792 to 583 computations (26.4% saved)

Details

analyze3.0ms (0%)

sample25.0ms (0%)

simplify344.0ms (0.5%)

prune7.0ms (0%)

localize8.0ms (0%)

rewrite35.0ms (0%)

series382.0ms (0.5%)

simplify79.0ms (0.1%)

prune151.0ms (0.2%)

localize9.0ms (0%)

rewrite49.0ms (0.1%)

series510.0ms (0.7%)

simplify70.0ms (0.1%)

prune396.0ms (0.6%)

localize14.0ms (0%)

rewrite122.0ms (0.2%)

series1.1min (88.1%)

simplify370.0ms (0.5%)

prune4.1s (5.7%)

localize6.0ms (0%)

rewrite8.0ms (0%)

series84.0ms (0.1%)

simplify70.0ms (0.1%)

prune36.0ms (0.1%)

regimes319.0ms (0.4%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (1.9%)

Profiling