Details

analyze651.0ms (13.6%)

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
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	62×	body	80	invalid

Compiler

Compiled 23 to 25 computations (-8.7% saved)

simplify340.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (325.0ms)

Iter	Nodes	Cost
0	1485	16
1	1485	16

prune5.0ms (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: 4.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(/.f64 t (-.f64 1 z))
4.6b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite55.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
12×	`distribute-lft-out--_binary64`
10×	`associate-r_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`associate-/r/_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 90

Calls

3 calls:

23.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
22.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
6.0ms	(/.f64 t (-.f64 1 z))

series31.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

16.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
9.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
6.0ms	(/.f64 t (-.f64 1 z))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5443	1707

prune112.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	86	13	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	13	100

Merged error: 0.0b

Counts

100 → 13

Compiler

Compiled 2128 to 1114 computations (47.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 t)
0.5b	(cbrt.f64 t)
0.5b	(cbrt.f64 t)
4.6b	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (/.f64 (cbrt.f64 t) (cbrt.f64 (-.f64 1 z))))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`pow1_binary64` `associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `frac-sub_binary64`
2×	`sub-neg_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

10.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (/.f64 (cbrt.f64 t) (cbrt.f64 (-.f64 1 z))))))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series67.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (/.f64 (cbrt.f64 t) (cbrt.f64 (-.f64 1 z))))))
16.0ms	(cbrt.f64 t)
15.0ms	(cbrt.f64 t)
14.0ms	(cbrt.f64 t)

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4958	825
1	4958	825

prune86.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	70	13	83

Merged error: 0.0b

Counts

83 → 13

Compiler

Compiled 2366 to 1326 computations (44% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
2.3b	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
2.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))

rewrite60.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`pow1_binary64` `add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-l_binary64`
10×	`cbrt-prod_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
8×	`times-frac_binary64`
7×	`associate-r_binary64`
6×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`associate-*r/_binary64`
2×	`flip3--_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

31.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
24.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series87.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
21.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5235	1464

prune82.0ms (1.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	91	13	104

Merged error: 0.0b

Counts

104 → 13

Compiler

Compiled 2274 to 1045 computations (54% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
7.0b	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
7.0b	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
7.0b	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite114.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
107×	`add-sqr-sqrt_binary64`
82×	`cbrt-prod_binary64`
64×	`times-frac_binary64`
36×	`distribute-lft-out--_binary64`
33×	`cbrt-div_binary64`
28×	`difference-of-squares_binary64`
17×	`swap-sqr_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
11×	`pow1_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
9×	`pow1/3_binary64` `frac-times_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 143

Calls

4 calls:

47.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
21.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
19.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
19.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series153.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
38.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
34.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
34.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

simplify107.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5411	4835

prune209.0ms (4.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	155	13	168

Merged error: 0.0b

Counts

168 → 13

Compiler

Compiled 6670 to 3640 computations (45.4% saved)

regimes555.0ms (11.6%)

Compiler: Compiled 2186 to 1632 computations (25.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 9 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	135	106
1	135	106

end0.0ms (0%)

sample1.7s (36.1%)

Algorithm

1×

intervals

Results

285.0ms	8000×	body	80	valid
61.0ms	1821×	body	80	invalid

Compiler

Compiled 465 to 332 computations (28.6% saved)

Details

analyze651.0ms (13.6%)

sample22.0ms (0.5%)

simplify340.0ms (7.1%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

rewrite55.0ms (1.1%)

series31.0ms (0.6%)

simplify83.0ms (1.7%)

prune112.0ms (2.4%)

localize15.0ms (0.3%)

rewrite15.0ms (0.3%)

series67.0ms (1.4%)

simplify104.0ms (2.2%)

prune86.0ms (1.8%)

localize11.0ms (0.2%)

rewrite60.0ms (1.3%)

series87.0ms (1.8%)

simplify64.0ms (1.3%)

prune82.0ms (1.7%)

localize12.0ms (0.2%)

rewrite114.0ms (2.4%)

series153.0ms (3.2%)

simplify107.0ms (2.2%)

prune209.0ms (4.4%)

regimes555.0ms (11.6%)

bsearch1.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.7s (36.1%)

Profiling