Details

analyze3.7s (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample117.0ms (0.4%)

Algorithm

1×

intervals

Results

47.0ms	256×	body	128	valid
23.0ms	130×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify255.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5053	44

prune10.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.2b

Counts

2 → 1

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize54.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2/3 t)
1.6b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.4b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite95.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_11694`
33×	`*-un-lft-identity_binary64_11672`
31×	`add-cube-cbrt_binary64_11707`
30×	`times-frac_binary64_11678` `associate--r+_binary64_11608`
27×	`cancel-sign-sub-inv_binary64_11638`
20×	`frac-sub_binary64_11681`
15×	`distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622`
13×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
9×	`flip3--_binary64_11676` `flip--_binary64_11647`
8×	`frac-times_binary64_11682` `associate-*r/_binary64_11614`
7×	`associate-r_binary64_11612`
6×	`pow1_binary64_11733` `add-log-exp_binary64_11711` `associate-/r*_binary64_11616`
5×	`flip-+_binary64_11646` `flip3-+_binary64_11675` `sqrt-prod_binary64_11688`
4×	`sqrt-div_binary64_11689` `div-inv_binary64_11669` `associate-/l*_binary64_11617`
3×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723` `sub-neg_binary64_11665` `associate-l_binary64_11613`
2×	`cbrt-unprod_binary64_11705` `clear-num_binary64_11671` `associate--l+_binary64_11609` `associate-*l/_binary64_11615` `unswap-sqr_binary64_11640` `prod-exp_binary64_11721` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619`
1×	`distribute-lft-out_binary64_11623` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743` `diff-log_binary64_11764`

Counts

4 → 131

Calls

4 calls:

31.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
16.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
13.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
6.0ms	(/.f64 2/3 t)

series579.0ms (2%)

Counts

4 → 12

Calls

4 calls:

354.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
117.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
87.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
21.0ms	(/.f64 2/3 t)

simplify192.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4945	3630
1	4945	3630

prune463.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	3	144

Merged error: 0b

Counts

144 → 3

Compiler

Compiled 5781 to 2869 computations (50.4% saved)

localize59.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.1b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
1.6b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))

rewrite190.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64_11694`
76×	`times-frac_binary64_11678`
61×	`*-un-lft-identity_binary64_11672`
60×	`frac-sub_binary64_11681`
49×	`add-cube-cbrt_binary64_11707`
46×	`associate-r_binary64_11612`
39×	`frac-times_binary64_11682`
31×	`cbrt-prod_binary64_11703`
30×	`associate--r+_binary64_11608`
28×	`sqrt-prod_binary64_11688`
27×	`cancel-sign-sub-inv_binary64_11638` `associate-*r/_binary64_11614`
25×	`flip3--_binary64_11676` `add-exp-log_binary64_11710` `flip--_binary64_11647`
21×	`associate-*l/_binary64_11615`
18×	`add-cbrt-cube_binary64_11708`
15×	`distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622`
10×	`unswap-sqr_binary64_11640`
9×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
8×	`cbrt-unprod_binary64_11705` `prod-exp_binary64_11721`
7×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723` `associate-l_binary64_11613`
6×	`pow1_binary64_11733` `add-log-exp_binary64_11711` `distribute-lft-out_binary64_11623`
4×	`div-inv_binary64_11669`
3×	`sub-neg_binary64_11665`
2×	`associate--l+_binary64_11609` `pow1/3_binary64_11754`
1×	`*-commutative_binary64_11603` `pow-prod-down_binary64_11743` `diff-log_binary64_11764`

Counts

4 → 193

Calls

4 calls:

53.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
53.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
2.0ms	(cbrt.f64 t)
2.0ms	(cbrt.f64 t)

series999.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

469.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
215.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
159.0ms	(cbrt.f64 t)
155.0ms	(cbrt.f64 t)

simplify176.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5061	8091

prune808.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	205	3	208

Merged error: 0b

Counts

208 → 3

Compiler

Compiled 10185 to 5000 computations (50.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 a 5/6)
0.0b	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
0.1b	(*.f64 c (+.f64 a 5/6))
0.6b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_11694`
16×	`associate-r_binary64_11612`
15×	`*-un-lft-identity_binary64_11672`
10×	`add-exp-log_binary64_11710`
9×	`add-cube-cbrt_binary64_11707`
8×	`add-log-exp_binary64_11711` `add-cbrt-cube_binary64_11708`
6×	`pow1_binary64_11733` `unpow-prod-down_binary64_11751` `associate-l_binary64_11613`
5×	`unswap-sqr_binary64_11640`
4×	`associate--l+_binary64_11609` `prod-exp_binary64_11721` `unpow-prod-up_binary64_11750`
3×	`distribute-lft-in_binary64_11621` `associate-*r/_binary64_11614` `distribute-rgt-in_binary64_11622`
2×	`cbrt-unprod_binary64_11705` `cancel-sign-sub-inv_binary64_11638` `flip-+_binary64_11646` `flip3-+_binary64_11675` `sqr-pow_binary64_11644` `exp-lft-sqr_binary64_11727` `distribute-lft-out_binary64_11623` `*-commutative_binary64_11603` `sub-neg_binary64_11665`
1×	`pow-sub_binary64_11748` `pow-exp_binary64_11740` `pow-to-exp_binary64_11741` `sum-log_binary64_11763` `+-commutative_binary64_11602` `flip3--_binary64_11676` `flip--_binary64_11647` `pow-prod-down_binary64_11743` `diff-log_binary64_11764`

Counts

4 → 81

Calls

4 calls:

16.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
13.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
13.0ms	(*.f64 c (+.f64 a 5/6))
6.0ms	(+.f64 a 5/6)

series321.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
51.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
37.0ms	(*.f64 c (+.f64 a 5/6))
24.0ms	(+.f64 a 5/6)

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4916	1421
1	4916	1421

prune205.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Merged error: 0b

Counts

96 → 3

Compiler

Compiled 2226 to 1306 computations (41.3% saved)

localize64.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
4.9b	(.f64 t (-.f64 (.f64 a a) 25/36))
5.1b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
29.9b	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

rewrite863.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1530×	`associate-*r/_binary64_11614`
768×	`frac-sub_binary64_11681`
713×	`flip3--_binary64_11676` `flip--_binary64_11647`
528×	`frac-times_binary64_11682`
360×	`sqrt-div_binary64_11689`
180×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
168×	`associate-*l/_binary64_11615`
162×	`associate-/l/_binary64_11619`
44×	`distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622`
41×	`cancel-sign-sub-inv_binary64_11638`
40×	`associate--l+_binary64_11609`
29×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
25×	`add-sqr-sqrt_binary64_11694`
20×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672` `associate--r+_binary64_11608`
17×	`sub-neg_binary64_11665`
11×	`cbrt-unprod_binary64_11705` `prod-exp_binary64_11721`
8×	`pow1_binary64_11733`
7×	`associate-r_binary64_11612`
6×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723` `add-log-exp_binary64_11711` `associate-l_binary64_11613`
2×	`associate-/r/_binary64_11618` `unswap-sqr_binary64_11640` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743`
1×	`clear-num_binary64_11671` `associate-/r_binary64_11616` `times-frac_binary64_11678` `frac-2neg_binary64_11683` `difference-of-squares_binary64_11641` `div-inv_binary64_11669` `associate-/l_binary64_11617` `diff-log_binary64_11764`

Counts

4 → 618

Calls

4 calls:

124.0ms	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))
99.0ms	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
62.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
17.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))

series3.7s (12.5%)

Counts

4 → 12

Calls

4 calls:

1.5s	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))
1.2s	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
861.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
76.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))

simplify894.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5190	65959

prune8.6s (29.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	630	0	630
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	630	3	633

Merged error: 0b

Counts

633 → 3

Compiler

Compiled 77542 to 40425 computations (47.9% saved)

regimes1.6s (5.5%)

Compiler: Compiled 12284 to 9760 computations (20.5% saved)

bsearch166.0ms (0.6%)

Steps

Iters	Range		Point
8	1443628.7219269546	8993773518.24429	407588222.4321934
6	1.11166721441719e-111	7.474181282389385e-111	1.4194606864782556e-111

Compiler

Compiled 1 to 7 computations (-600% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	804	177
1	804	177

end0.0ms (0%)

sample5.0s (17%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
894.0ms	4885×	body	128	nan

Compiler

Compiled 1194 to 920 computations (22.9% saved)

Details

analyze3.7s (12.6%)

sample117.0ms (0.4%)

simplify255.0ms (0.9%)

prune10.0ms (0%)

localize54.0ms (0.2%)

rewrite95.0ms (0.3%)

series579.0ms (2%)

simplify192.0ms (0.7%)

prune463.0ms (1.6%)

localize59.0ms (0.2%)

rewrite190.0ms (0.6%)

series999.0ms (3.4%)

simplify176.0ms (0.6%)

prune808.0ms (2.8%)

localize29.0ms (0.1%)

rewrite65.0ms (0.2%)

series321.0ms (1.1%)

simplify128.0ms (0.4%)

prune205.0ms (0.7%)

localize64.0ms (0.2%)

rewrite863.0ms (2.9%)

series3.7s (12.5%)

simplify894.0ms (3.1%)

prune8.6s (29.3%)

regimes1.6s (5.5%)

bsearch166.0ms (0.6%)

simplify61.0ms (0.2%)

end0.0ms (0%)

sample5.0s (17%)

Profiling