Details

analyze1.1s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	211×	body	80	valid
2.0ms	12×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	24×	body	80	invalid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify191.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4895	19
1	4895	19

prune7.0ms (0.1%)

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: 15.7b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 z t) y)
1.4b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.1b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `associate-l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
4×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 69

Calls

3 calls:

13.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
12.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
8.0ms	(*.f64 (-.f64 z t) y)

series76.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
21.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
8.0ms	(*.f64 (-.f64 z t) y)

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4994	1279
1	4994	1279

prune114.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	12	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	12	79

Merged error: 5.8b

Counts

79 → 12

Compiler

Compiled 1637 to 452 computations (72.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
2.7b	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
8.0b	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

rewrite67.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
30×	`associate-r_binary64`
27×	`cbrt-prod_binary64`
25×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
9×	`add-log-exp_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

43.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
8.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))
4.0ms	(cbrt.f64 (-.f64 a t))
4.0ms	(cbrt.f64 (-.f64 a t))

series145.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))
35.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
32.0ms	(cbrt.f64 (-.f64 a t))
28.0ms	(cbrt.f64 (-.f64 a t))

simplify135.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5706	3563

prune132.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	136	14	150

Merged error: 5.8b

Counts

150 → 14

Compiler

Compiled 4423 to 916 computations (79.3% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

4.2b	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
4.2b	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
4.2b	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
8.7b	(-.f64 (+.f64 x y) (.f64 (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))))

rewrite74.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`cbrt-prod_binary64`
72×	`times-frac_binary64`
67×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
57×	`cbrt-div_binary64`
49×	`add-cube-cbrt_binary64`
34×	`frac-times_binary64`
30×	`frac-sub_binary64`
26×	`associate-*l/_binary64`
22×	`associate-*r/_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
9×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r/_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/3_binary64` `div-inv_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 160

Calls

4 calls:

21.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))))
14.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
11.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
11.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))

series246.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))))
62.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
51.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
50.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5554	7120

prune162.0ms (2.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	166	6	172
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	171	15	186

Merged error: 5.6b

Counts

186 → 15

Compiler

Compiled 9529 to 1531 computations (83.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
2.7b	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
14.5b	(-.f64 y (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
30×	`associate-r_binary64`
27×	`cbrt-prod_binary64`
25×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`frac-times_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `*-commutative_binary64`

Counts

4 → 118

Calls

4 calls:

33.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
6.0ms	(cbrt.f64 (-.f64 a t))
4.0ms	(-.f64 y (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))
4.0ms	(cbrt.f64 (-.f64 a t))

series113.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt.f64 (-.f64 a t))
29.0ms	(-.f64 y (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))
27.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
27.0ms	(cbrt.f64 (-.f64 a t))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4960	3057
1	4960	3057

prune76.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	130	15	145

Merged error: 5.6b

Counts

145 → 15

Compiler

Compiled 3768 to 769 computations (79.6% saved)

regimes490.0ms (8.2%)

Compiler: Compiled 2225 to 1245 computations (44% saved)

bsearch37.0ms (0.6%)

Steps

Iters	Range		Point
5	3.841001760825762e-115	8.240112780336763e-115	6.542204967337177e-115
7	-9.54158598619668e-162	-1.0000678501546393e-163	-1.438849187731562e-163

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	111	79
1	111	79

end0.0ms (0%)

sample2.3s (38.8%)

Algorithm

1×

intervals

Results

309.0ms	6635×	body	80	valid
73.0ms	456×	body	640	valid
61.0ms	262×	body	1280	valid
47.0ms	389×	body	320	valid
31.0ms	727×	body	80	invalid
20.0ms	239×	body	160	valid
5.0ms	19×	body	2560	valid

Compiler

Compiled 583 to 316 computations (45.8% saved)

Details

analyze1.1s (18.6%)

sample30.0ms (0.5%)

simplify191.0ms (3.2%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series76.0ms (1.3%)

simplify83.0ms (1.4%)

prune114.0ms (1.9%)

localize15.0ms (0.3%)

rewrite67.0ms (1.1%)

series145.0ms (2.4%)

simplify135.0ms (2.3%)

prune132.0ms (2.2%)

localize29.0ms (0.5%)

rewrite74.0ms (1.2%)

series246.0ms (4.1%)

simplify105.0ms (1.8%)

prune162.0ms (2.7%)

localize14.0ms (0.2%)

rewrite53.0ms (0.9%)

series113.0ms (1.9%)

simplify95.0ms (1.6%)

prune76.0ms (1.3%)

regimes490.0ms (8.2%)

bsearch37.0ms (0.6%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.3s (38.8%)

Profiling