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)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	pre	128	true
6.0ms	190×	body	128	valid
4.0ms	31×	body	1024	valid
1.0ms	14×	body	512	valid
1.0ms	17×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify346.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (251.0ms)

Iter	Nodes	Cost
0	5018	19

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

Merged error: 16.4b

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))
2.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite39.0ms (0.6%)

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:

23.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series76.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

45.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
31.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6172	1488

prune92.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 15.4b

Counts

72 → 10

Compiler

Compiled 1716 to 971 computations (43.4% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
2.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite65.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

32.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series122.0ms (2%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
46.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
27.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4940	2303
1	4940	2303

prune146.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	102	8	110

Merged error: 4.0b

Counts

110 → 8

Compiler

Compiled 2955 to 1785 computations (39.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
0.1b	(/.f64 (-.f64 (+.f64 beta (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
2.9b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
6.4b	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite131.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64_2465`
54×	`add-sqr-sqrt_binary64_2487`
39×	`times-frac_binary64_2471`
27×	`add-cube-cbrt_binary64_2500` `cube-prod_binary64_2493` `unpow-prod-down_binary64_2544`
24×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
21×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
18×	`associate-/l/_binary64_2412` `distribute-lft-out_binary64_2416`
16×	`frac-sub_binary64_2474`
14×	`frac-times_binary64_2475`
13×	`associate-*r/_binary64_2407`
12×	`difference-of-squares_binary64_2434` `associate-/r/_binary64_2411`
10×	`pow1_binary64_2526`
8×	`flip--_binary64_2440` `flip3--_binary64_2469`
7×	`associate-*l/_binary64_2408`
6×	`add-log-exp_binary64_2504` `difference-of-sqr-1_binary64_2435` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
4×	`distribute-lft-in_binary64_2414` `cbrt-undiv_binary64_2499` `distribute-rgt-in_binary64_2415` `div-exp_binary64_2516` `sqr-pow_binary64_2437`
3×	`cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `pow-prod-down_binary64_2536` `pow-unpow_binary64_2542` `associate-/l_binary64_2410` `associate-l*_binary64_2406`
2×	`rem-cube-cbrt_binary64_2488` `pow-exp_binary64_2533`
1×	`unpow3_binary64_2531` `-commutative_binary64_2396` `associate-/r_binary64_2409` `clear-num_binary64_2464` `div-sub_binary64_2470` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `cube-mult_binary64_2495` `pow-to-exp_binary64_2534` `diff-log_binary64_2557` `pow-pow_binary64_2537` `frac-2neg_binary64_2476` `associate-r_binary64_2405` `cube-div_binary64_2494`

Counts

4 → 172

Calls

4 calls:

28.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
26.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
22.0ms	(/.f64 (-.f64 (+.f64 beta (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
10.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)

series503.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

309.0ms	(/.f64 (-.f64 (+.f64 beta (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
77.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)
69.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
48.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5032	8516

prune880.0ms (14.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	183	9	192

Merged error: 4.0b

Counts

192 → 9

Compiler

Compiled 17013 to 9996 computations (41.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.8b	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
2.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
9.4b	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite101.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_2465`
39×	`add-sqr-sqrt_binary64_2487`
20×	`times-frac_binary64_2471`
18×	`add-cube-cbrt_binary64_2500`
14×	`log-prod_binary64_2551`
12×	`distribute-lft-out_binary64_2416`
8×	`log-div_binary64_2552` `difference-of-squares_binary64_2434`
7×	`add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `exp-sum_binary64_2511`
6×	`add-log-exp_binary64_2504` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
5×	`associate-/r*_binary64_2409` `flip--_binary64_2440` `flip3--_binary64_2469`
4×	`exp-prod_binary64_2517` `exp-diff_binary64_2513` `frac-sub_binary64_2474`
3×	`cancel-sign-sub-inv_binary64_2431` `associate-/l*_binary64_2410`
2×	`difference-of-sqr-1_binary64_2435` `log-pow_binary64_2554` `associate-/r/_binary64_2411`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `rem-exp-log_binary64_2505` `rem-log-exp_binary64_2506`

Counts

4 → 101

Calls

4 calls:

36.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
31.0ms	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series234.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
75.0ms	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
51.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
26.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4909	3070
1	4909	3070

prune152.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Merged error: 4.0b

Counts

122 → 10

Compiler

Compiled 3423 to 2118 computations (38.1% saved)

regimes654.0ms (10.7%)

Compiler: Compiled 10870 to 7402 computations (31.9% saved)

bsearch4.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	187	87
1	187	87

end0.0ms (0%)

sample2.1s (35.1%)

Algorithm

1×

intervals

Results

202.0ms	5959×	body	128	valid
147.0ms	8000×	pre	128	true
135.0ms	1014×	body	1024	valid
58.0ms	595×	body	512	valid
25.0ms	342×	body	256	valid
17.0ms	90×	body	2048	valid

Compiler

Compiled 2238 to 1526 computations (31.8% saved)

Details

analyze3.0ms (0%)

sample30.0ms (0.5%)

simplify346.0ms (5.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite39.0ms (0.6%)

series76.0ms (1.2%)

simplify69.0ms (1.1%)

prune92.0ms (1.5%)

localize11.0ms (0.2%)

rewrite65.0ms (1.1%)

series122.0ms (2%)

simplify65.0ms (1.1%)

prune146.0ms (2.4%)

localize19.0ms (0.3%)

rewrite131.0ms (2.2%)

series503.0ms (8.3%)

simplify91.0ms (1.5%)

prune880.0ms (14.5%)

localize13.0ms (0.2%)

rewrite101.0ms (1.7%)

series234.0ms (3.8%)

simplify91.0ms (1.5%)

prune152.0ms (2.5%)

regimes654.0ms (10.7%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.1s (35.1%)

Profiling