Details

analyze256.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample65.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	70×	body	1024	valid
17.0ms	39×	body	2048	valid
8.0ms	41×	body	512	valid
4.0ms	90×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify162.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 49.1b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
0.4b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2487`
8×	`add-log-exp_binary64_2526`
7×	`add-sqr-sqrt_binary64_2509`
6×	`add-cube-cbrt_binary64_2522` `pow1_binary64_2548`
5×	`add-exp-log_binary64_2525`
4×	`flip-+_binary64_2461` `flip3-+_binary64_2490` `add-cbrt-cube_binary64_2523` `log-prod_binary64_2573`
3×	`sqrt-prod_binary64_2503`
2×	`distribute-lft-out_binary64_2438` `+-commutative_binary64_2417` `sum-log_binary64_2578` `log-div_binary64_2574` `sqrt-div_binary64_2504`
1×	`rem-log-exp_binary64_2528` `sqrt-pow1_binary64_2505` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567` `log-pow_binary64_2576`

Counts

4 → 53

Calls

4 calls:

8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(+.f64 (*.f64 x x) 1)

series227.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
52.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
48.0ms	(+.f64 (*.f64 x x) 1)
36.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4837	1001
1	4837	1001

prune234.0ms (4.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

Compiler

Compiled 3461 to 2491 computations (28% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.3b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2509`
15×	`associate-l_binary64_2428`
14×	`add-exp-log_binary64_2525`
11×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `add-log-exp_binary64_2526`
10×	`associate-r_binary64_2427`
8×	`unpow-prod-down_binary64_2566` `add-cbrt-cube_binary64_2523`
7×	`unswap-sqr_binary64_2455`
6×	`prod-exp_binary64_2536`
4×	`cube-prod_binary64_2515` `pow1_binary64_2548` `sqr-pow_binary64_2459`
2×	`pow-exp_binary64_2555` `*-commutative_binary64_2418` `diff-log_binary64_2579` `pow-to-exp_binary64_2556` `sum-log_binary64_2578` `cbrt-unprod_binary64_2520`
1×	`flip--_binary64_2462` `sub-neg_binary64_2480` `unpow3_binary64_2553` `cancel-sign-sub-inv_binary64_2453` `associate--l+_binary64_2424` `flip-+_binary64_2461` `+-commutative_binary64_2417` `flip3-+_binary64_2490` `cube-mult_binary64_2517` `flip3--_binary64_2491`

Counts

4 → 81

Calls

4 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series347.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
74.0ms	(*.f64 3/40 (pow.f64 x 5))
54.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
46.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5018	1208

prune102.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

Compiler

Compiled 1725 to 1335 computations (22.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.6b	(/.f64 1/8 (pow.f64 x 3))
10.5b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite121.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64_2493`
97×	`*-un-lft-identity_binary64_2487`
87×	`add-sqr-sqrt_binary64_2509`
80×	`cancel-sign-sub-inv_binary64_2453`
74×	`add-cube-cbrt_binary64_2522`
42×	`associate-+r+_binary64_2419`
31×	`unpow-prod-down_binary64_2566` `cube-prod_binary64_2515`
18×	`add-log-exp_binary64_2526`
12×	`associate-/r*_binary64_2431`
11×	`sqr-pow_binary64_2459`
10×	`add-exp-log_binary64_2525` `unpow3_binary64_2553` `cube-mult_binary64_2517`
9×	`distribute-lft-out_binary64_2438`
6×	`distribute-lft-out--_binary64_2439` `add-cbrt-cube_binary64_2523` `log-prod_binary64_2573`
5×	`difference-of-squares_binary64_2456` `sum-log_binary64_2578` `pow1_binary64_2548`
4×	`diff-log_binary64_2579`
3×	`associate-/l*_binary64_2432` `flip-+_binary64_2461` `div-inv_binary64_2484` `flip3-+_binary64_2490` `div-exp_binary64_2538`
2×	`sub-neg_binary64_2480` `frac-sub_binary64_2496` `associate--l+_binary64_2424` `log-div_binary64_2574`
1×	`pow-exp_binary64_2555` `flip--_binary64_2462` `pow-to-exp_binary64_2556` `frac-2neg_binary64_2498` `rem-log-exp_binary64_2528` `clear-num_binary64_2486` `+-commutative_binary64_2417` `associate-+r-_binary64_2421` `log-pow_binary64_2576` `flip3--_binary64_2491` `cbrt-undiv_binary64_2521`

Counts

4 → 203

Calls

4 calls:

36.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
28.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
26.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series201.0ms (4%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
46.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
42.0ms	(/.f64 1/8 (pow.f64 x 3))
39.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4933	3378
1	4933	3378

prune273.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	215	5	220

Merged error: 0.0b

Counts

220 → 5

Compiler

Compiled 4430 to 3179 computations (28.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
2.2b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
14.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`sqrt-prod_binary64_2503` `*-un-lft-identity_binary64_2487` `log-prod_binary64_2573`
12×	`add-sqr-sqrt_binary64_2509`
10×	`add-cube-cbrt_binary64_2522` `pow1_binary64_2548`
8×	`sqrt-div_binary64_2504`
6×	`add-exp-log_binary64_2525` `log-pow_binary64_2576`
4×	`flip-+_binary64_2461` `sqrt-pow1_binary64_2505` `flip3-+_binary64_2490` `add-cbrt-cube_binary64_2523` `log-div_binary64_2574` `add-log-exp_binary64_2526` `pow1/2_binary64_2567`
2×	`distribute-lft-out_binary64_2438` `rem-log-exp_binary64_2528` `rem-sqrt-square_binary64_2500`

Counts

4 → 70

Calls

4 calls:

8.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
8.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series209.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
71.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
31.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
31.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4810	1612
1	4810	1612

prune107.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	82	5	87

Merged error: 0.0b

Counts

87 → 5

Compiler

Compiled 2270 to 1484 computations (34.6% saved)

regimes43.0ms (0.9%)

Compiler: Compiled 168 to 134 computations (20.2% saved)

bsearch37.0ms (0.7%)

Steps

Iters	Range		Point
8	0.0007531855139248682	23.575992414981645	0.9475279190554214
9	-1680000.618228654	-0.016292050559205556	-1.0860109172826882

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (43.1%)

Algorithm

1×

intervals

Results

957.0ms	2516×	body	1024	valid
389.0ms	1157×	body	2048	valid
265.0ms	1262×	body	512	valid
111.0ms	2374×	body	128	valid
74.0ms	648×	body	256	valid
20.0ms	43×	body	4096	valid

Compiler

Compiled 160 to 126 computations (21.3% saved)

Details

analyze256.0ms (5.1%)

sample65.0ms (1.3%)

simplify162.0ms (3.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite28.0ms (0.6%)

series227.0ms (4.5%)

simplify78.0ms (1.6%)

prune234.0ms (4.7%)

localize9.0ms (0.2%)

rewrite32.0ms (0.6%)

series347.0ms (6.9%)

simplify63.0ms (1.3%)

prune102.0ms (2%)

localize10.0ms (0.2%)

rewrite121.0ms (2.4%)

series201.0ms (4%)

simplify91.0ms (1.8%)

prune273.0ms (5.5%)

localize9.0ms (0.2%)

rewrite33.0ms (0.7%)

series209.0ms (4.2%)

simplify92.0ms (1.8%)

prune107.0ms (2.1%)

regimes43.0ms (0.9%)

bsearch37.0ms (0.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (43.1%)

Profiling