Details

analyze3.0ms (0.1%)

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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	198×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	30×	body	1024	valid
2.0ms	21×	body	512	valid
0.0ms	3×	body	2048	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify315.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	5139	19

prune2.0ms (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

Merged error: 14.6b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

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)

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2487`
26×	`add-sqr-sqrt_binary64_2509`
25×	`times-frac_binary64_2493`
19×	`distribute-lft-out_binary64_2438`
14×	`add-cube-cbrt_binary64_2522`
6×	`difference-of-squares_binary64_2456` `distribute-lft-out--_binary64_2439`
5×	`associate-/r_binary64_2431` `associate-/l_binary64_2432`
4×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `add-log-exp_binary64_2526`
2×	`associate-/r/_binary64_2433` `flip-+_binary64_2461` `div-sub_binary64_2492` `flip3-+_binary64_2490` `pow1_binary64_2548` `associate-/l/_binary64_2434`
1×	`flip--_binary64_2462` `associate-+l-_binary64_2422` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `+-commutative_binary64_2417` `sum-log_binary64_2578` `div-exp_binary64_2538` `flip3--_binary64_2491` `cbrt-undiv_binary64_2521`

Counts

2 → 65

Calls

2 calls:

21.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series165.0ms (3%)

Counts

2 → 6

Calls

2 calls:

96.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
70.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5220	1488

prune261.0ms (4.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 14.0b

Counts

72 → 11

Compiler

Compiled 5307 to 3473 computations (34.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
1.5b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite88.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`*-un-lft-identity_binary64_2487`
68×	`add-sqr-sqrt_binary64_2509`
58×	`times-frac_binary64_2493`
37×	`add-cube-cbrt_binary64_2522`
24×	`distribute-lft-out_binary64_2438`
13×	`associate-/r_binary64_2431` `associate-/l_binary64_2432` `distribute-lft-out--_binary64_2439`
12×	`difference-of-squares_binary64_2456`
10×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
6×	`add-log-exp_binary64_2526`
4×	`associate-/r/_binary64_2433` `pow1_binary64_2548` `associate-/l/_binary64_2434`
3×	`flip--_binary64_2462` `cancel-sign-sub-inv_binary64_2453` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `div-exp_binary64_2538` `flip3--_binary64_2491` `cbrt-undiv_binary64_2521`
2×	`frac-sub_binary64_2496` `difference-of-sqr-1_binary64_2457` `flip-+_binary64_2461` `flip3-+_binary64_2490`
1×	`sub-neg_binary64_2480` `diff-log_binary64_2579` `div-sub_binary64_2492`

Counts

4 → 143

Calls

4 calls:

37.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
18.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series334.0ms (6%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
104.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
61.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
59.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5352	3804

prune895.0ms (16.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	10	155
Fresh	10	0	10
Picked	0	1	1
Done	0	0	0
Total	155	11	166

Merged error: 2.9b

Counts

166 → 11

Compiler

Compiled 19526 to 13379 computations (31.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
1.5b	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite100.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`*-un-lft-identity_binary64_2487`
130×	`times-frac_binary64_2493`
96×	`distribute-lft-out_binary64_2438`
84×	`add-sqr-sqrt_binary64_2509`
72×	`add-cube-cbrt_binary64_2522`
39×	`swap-sqr_binary64_2454`
21×	`associate-l_binary64_2428` `associate-r_binary64_2427`
20×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
12×	`associate-/r/_binary64_2433`
11×	`pow1_binary64_2548`
10×	`associate-/r*_binary64_2431`
7×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
6×	`associate-/l*_binary64_2432` `div-inv_binary64_2484` `div-exp_binary64_2538` `add-log-exp_binary64_2526` `cbrt-undiv_binary64_2521`
4×	`unswap-sqr_binary64_2455` `prod-exp_binary64_2536` `cbrt-unprod_binary64_2520`
2×	`frac-2neg_binary64_2498` `clear-num_binary64_2486`
1×	`associate-l/_binary64_2430` `-commutative_binary64_2418` `frac-times_binary64_2497` `pow-plus_binary64_2550` `pow-prod-up_binary64_2557` `difference-of-sqr--1_binary64_2458` `pow-sqr_binary64_2460` `pow2_binary64_2568` `+-commutative_binary64_2417` `sum-log_binary64_2578` `pow-prod-down_binary64_2558` `associate-*r/_binary64_2429`

Counts

4 → 195

Calls

4 calls:

32.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
19.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series329.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)
76.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
59.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
56.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4949	4118
1	4949	4118

prune441.0ms (7.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	207	11	218

Merged error: 2.9b

Counts

218 → 11

Compiler

Compiled 9595 to 5619 computations (41.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.6b	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
1.5b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
7.1b	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))

rewrite116.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64_2487`
79×	`add-sqr-sqrt_binary64_2509`
66×	`times-frac_binary64_2493`
50×	`log-prod_binary64_2573`
38×	`add-cube-cbrt_binary64_2522`
25×	`exp-sum_binary64_2533`
19×	`distribute-lft-out--_binary64_2439`
16×	`difference-of-squares_binary64_2456`
12×	`distribute-lft-out_binary64_2438`
9×	`add-exp-log_binary64_2525`
6×	`add-cbrt-cube_binary64_2523` `pow1_binary64_2548` `add-log-exp_binary64_2526`
5×	`associate-/r*_binary64_2431`
4×	`exp-prod_binary64_2539`
3×	`cancel-sign-sub-inv_binary64_2453` `associate-/l*_binary64_2432` `div-inv_binary64_2484`
2×	`associate-/r/_binary64_2433` `difference-of-sqr-1_binary64_2457` `rem-log-exp_binary64_2528` `div-exp_binary64_2538` `log-div_binary64_2574` `log-pow_binary64_2576`
1×	`flip--_binary64_2462` `sub-neg_binary64_2480` `diff-log_binary64_2579` `rem-exp-log_binary64_2527` `frac-2neg_binary64_2498` `exp-diff_binary64_2535` `flip-+_binary64_2461` `clear-num_binary64_2486` `flip3-+_binary64_2490` `flip3--_binary64_2491` `cbrt-undiv_binary64_2521`

Counts

4 → 132

Calls

4 calls:

40.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
34.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series586.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
181.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
96.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
66.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify129.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4926	4516
1	4926	4516

prune380.0ms (6.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	7	2	9
Picked	1	0	1
Done	0	1	1
Total	147	8	155

Merged error: 2.9b

Counts

155 → 8

Compiler

Compiled 8081 to 5443 computations (32.6% saved)

regimes69.0ms (1.2%)

Compiler: Compiled 526 to 398 computations (24.3% saved)

bsearch15.0ms (0.3%)

Steps

Iters	Range		Point
6	4.408790000714098e+18	4.9724012816074736e+19	4.470683226004296e+18

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	219	71
1	219	71

end0.0ms (0%)

sample975.0ms (17.6%)

Algorithm

1×

intervals

Results

198.0ms	5976×	body	128	valid
139.0ms	8000×	pre	128	true
131.0ms	1006×	body	1024	valid
56.0ms	583×	body	512	valid
20.0ms	320×	body	256	valid
18.0ms	115×	body	2048	valid

Compiler

Compiled 329 to 247 computations (24.9% saved)

Details

analyze3.0ms (0.1%)

sample24.0ms (0.4%)

simplify315.0ms (5.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite39.0ms (0.7%)

series165.0ms (3%)

simplify62.0ms (1.1%)

prune261.0ms (4.7%)

localize11.0ms (0.2%)

rewrite88.0ms (1.6%)

series334.0ms (6%)

simplify79.0ms (1.4%)

prune895.0ms (16.1%)

localize13.0ms (0.2%)

rewrite100.0ms (1.8%)

series329.0ms (5.9%)

simplify85.0ms (1.5%)

prune441.0ms (7.9%)

localize15.0ms (0.3%)

rewrite116.0ms (2.1%)

series586.0ms (10.6%)

simplify129.0ms (2.3%)

prune380.0ms (6.8%)

regimes69.0ms (1.2%)

bsearch15.0ms (0.3%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample975.0ms (17.6%)

Profiling