Details

analyze401.0ms (6.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4733	38
1	4733	38
0	2	2
1	2	2

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)

sample29.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	19×	body	512	valid
6.0ms	187×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	31×	body	1024	valid
1.0ms	17×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify253.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

Iter	Nodes	Cost
0	5018	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

Error

16.8b

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))
1.7b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite33.0ms (0.5%)

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:

18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series79.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
30.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	6172	1488

prune94.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Error

16.1b

Counts

72 → 12

Compiler

Compiled 1753 to 994 computations (43.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite102.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64_2465`
76×	`add-sqr-sqrt_binary64_2487`
47×	`times-frac_binary64_2471`
29×	`add-cube-cbrt_binary64_2500`
18×	`difference-of-squares_binary64_2434`
17×	`distribute-lft-out--_binary64_2417`
16×	`cancel-sign-sub-inv_binary64_2431`
12×	`distribute-lft-out_binary64_2416`
11×	`add-log-exp_binary64_2504`
10×	`associate-/l*_binary64_2410`
8×	`associate-/r*_binary64_2409` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
5×	`flip--_binary64_2440` `flip3--_binary64_2469`
4×	`associate--r+_binary64_2401` `difference-of-sqr-1_binary64_2435` `associate-/l/_binary64_2412` `diff-log_binary64_2557` `pow1_binary64_2526` `frac-sub_binary64_2474`
3×	`sub-neg_binary64_2458`
2×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `associate-/r/_binary64_2411` `frac-2neg_binary64_2476`
1×	`flip3-+_binary64_2468` `associate--r-_binary64_2404` `flip-+_binary64_2439` `div-sub_binary64_2470`

Counts

4 → 139

Calls

4 calls:

36.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
31.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series176.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
47.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
45.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
27.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4907	4383
1	4907	4383

prune223.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Error

2.8b

Counts

163 → 8

Compiler

Compiled 4674 to 2854 computations (38.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) 2)
0.0b	(/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.1b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
1.7b	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite184.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

363×	`*-un-lft-identity_binary64_2465`
222×	`times-frac_binary64_2471`
141×	`add-sqr-sqrt_binary64_2487`
113×	`distribute-lft-out_binary64_2416`
81×	`add-cube-cbrt_binary64_2500`
39×	`swap-sqr_binary64_2432`
28×	`distribute-lft-out--_binary64_2417`
21×	`associate-r_binary64_2405` `associate-l_binary64_2406`
20×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
18×	`associate-/l*_binary64_2410`
16×	`difference-of-squares_binary64_2434`
11×	`pow1_binary64_2526`
10×	`associate-/r/_binary64_2411`
7×	`flip3-+_binary64_2468` `associate-/r*_binary64_2409` `flip-+_binary64_2439`
6×	`add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499` `difference-of-sqr--1_binary64_2436` `div-exp_binary64_2516` `div-inv_binary64_2462`
5×	`associate-/l/_binary64_2412`
4×	`unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
2×	`clear-num_binary64_2464` `frac-2neg_binary64_2476`
1×	`associate-l/_binary64_2408` `-commutative_binary64_2396` `+-commutative_binary64_2395` `frac-times_binary64_2475` `pow-plus_binary64_2528` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-*r/_binary64_2407` `div-sub_binary64_2470` `pow2_binary64_2546` `pow-prod-down_binary64_2536` `flip3--_binary64_2469` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535` `frac-sub_binary64_2474`

Counts

4 → 236

Calls

4 calls:

61.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) 2)
38.0ms	(/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
25.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
17.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

series337.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) 2)
96.0ms	(/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
63.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)
44.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))

simplify143.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4942	9953
1	4942	9953

prune613.0ms (10.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	248	8	256

Error

2.8b

Counts

256 → 8

Compiler

Compiled 11583 to 7140 computations (38.4% saved)

localize12.0ms (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 alpha beta) 2)) 1)) 2)
0.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
7.9b	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))

rewrite132.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-sqr-sqrt_binary64_2487`
94×	`*-un-lft-identity_binary64_2465`
76×	`times-frac_binary64_2471`
50×	`log-prod_binary64_2551`
40×	`add-cube-cbrt_binary64_2500`
31×	`distribute-lft-out--_binary64_2417`
25×	`exp-sum_binary64_2511`
24×	`difference-of-squares_binary64_2434`
9×	`add-exp-log_binary64_2503`
7×	`associate-/l*_binary64_2410`
6×	`add-log-exp_binary64_2504` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
4×	`associate-/l/_binary64_2412` `exp-prod_binary64_2517`
3×	`associate-/r*_binary64_2409` `flip--_binary64_2440` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `flip3--_binary64_2469`
2×	`log-div_binary64_2552` `difference-of-sqr-1_binary64_2435` `log-pow_binary64_2554` `div-exp_binary64_2516` `rem-log-exp_binary64_2506` `frac-sub_binary64_2474`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `sub-neg_binary64_2458` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `rem-exp-log_binary64_2505` `exp-diff_binary64_2513`

Counts

4 → 143

Calls

4 calls:

37.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
33.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)
31.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

series292.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
82.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
52.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)
46.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

simplify115.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4916	5928
1	4916	5928

prune248.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Error

2.8b

Counts

163 → 8

Compiler

Compiled 5054 to 3267 computations (35.4% saved)

regimes516.0ms (8.5%)

Accuracy

Total 0.1b remaining (3.6%)

Threshold costs 0.1b (3.6%)

Compiler

Compiled 7700 to 5517 computations (28.4% saved)

bsearch3.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	214	101
1	214	101

end0.0ms (0%)

sample1.9s (31%)

Algorithm

1×

intervals

Results

194.0ms	5894×	body	128	valid
137.0ms	8000×	pre	128	true
135.0ms	1054×	body	1024	valid
55.0ms	585×	body	512	valid
23.0ms	364×	body	256	valid
20.0ms	103×	body	2048	valid

Compiler

Compiled 1614 to 1155 computations (28.4% saved)

Details

analyze401.0ms (6.6%)

sample29.0ms (0.5%)

simplify253.0ms (4.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite33.0ms (0.5%)

series79.0ms (1.3%)

simplify68.0ms (1.1%)

prune94.0ms (1.5%)

localize12.0ms (0.2%)

rewrite102.0ms (1.7%)

series176.0ms (2.9%)

simplify103.0ms (1.7%)

prune223.0ms (3.7%)

localize17.0ms (0.3%)

rewrite184.0ms (3%)

series337.0ms (5.5%)

simplify143.0ms (2.3%)

prune613.0ms (10.1%)

localize12.0ms (0.2%)

rewrite132.0ms (2.2%)

series292.0ms (4.8%)

simplify115.0ms (1.9%)

prune248.0ms (4.1%)

regimes516.0ms (8.5%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.9s (31%)

Profiling