Details

analyze1.3s (20.1%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	205×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	34×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4914	19
1	4914	19

prune6.0ms (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: 26.4b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
3.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
19.2b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 79

Calls

3 calls:

14.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
10.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

series103.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

55.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
38.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
10.0ms	(*.f64 (-.f64 y x) (-.f64 z t))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6017	1603

prune104.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 3.8b

Counts

89 → 11

Compiler

Compiled 1959 to 538 computations (72.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
2.4b	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
3.3b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

18.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

series146.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
42.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
10.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify134.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5070	2426

prune163.0ms (2.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	122	17	139

Merged error: 3.8b

Counts

139 → 17

Compiler

Compiled 2987 to 709 computations (76.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 z (-.f64 a t))
0.0b	(/.f64 t (-.f64 a t))
2.4b	(*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
3.3b	(+.f64 x (*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))

rewrite111.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out--_binary64`
18×	`associate-r_binary64`
15×	`difference-of-squares_binary64`
12×	`flip3--_binary64` `flip--_binary64`
10×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
5×	`associate-l_binary64`
4×	`sub-neg_binary64` `associate-*r/_binary64` `div-inv_binary64`
3×	`distribute-rgt-out--_binary64` `sub-div_binary64` `frac-sub_binary64`
2×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `associate-+r+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

66.0ms	(*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
13.0ms	(+.f64 x (*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))
11.0ms	(/.f64 t (-.f64 a t))
10.0ms	(/.f64 z (-.f64 a t))

series119.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(+.f64 x (*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))
42.0ms	(*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
8.0ms	(/.f64 z (-.f64 a t))
6.0ms	(/.f64 t (-.f64 a t))

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5274	2951

prune126.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	154	13	167

Merged error: 3.5b

Counts

167 → 13

Compiler

Compiled 3970 to 869 computations (78.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 t (-.f64 a t))
0.2b	(*.f64 z (/.f64 1 (-.f64 a t)))
2.4b	(.f64 (-.f64 y x) (-.f64 (.f64 z (/.f64 1 (-.f64 a t))) (/.f64 t (-.f64 a t))))
3.3b	(+.f64 x (.f64 (-.f64 y x) (-.f64 (.f64 z (/.f64 1 (-.f64 a t))) (/.f64 t (-.f64 a t)))))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`
17×	`add-exp-log_binary64`
13×	`associate-*r/_binary64` `add-cbrt-cube_binary64`
12×	`flip3--_binary64` `flip--_binary64` `frac-times_binary64`
8×	`pow1_binary64` `associate-l_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`un-div-inv_binary64`
6×	`add-log-exp_binary64` `sub-div_binary64` `frac-sub_binary64`
5×	`associate-/r*_binary64` `prod-exp_binary64`
4×	`sub-neg_binary64` `associate-/r/_binary64` `unswap-sqr_binary64`
3×	`cbrt-unprod_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `distribute-rgt-out--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 137

Calls

4 calls:

21.0ms	(.f64 (-.f64 y x) (-.f64 (.f64 z (/.f64 1 (-.f64 a t))) (/.f64 t (-.f64 a t))))
11.0ms	(*.f64 z (/.f64 1 (-.f64 a t)))
6.0ms	(/.f64 t (-.f64 a t))
4.0ms	(+.f64 x (.f64 (-.f64 y x) (-.f64 (.f64 z (/.f64 1 (-.f64 a t))) (/.f64 t (-.f64 a t)))))

series112.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(+.f64 x (.f64 (-.f64 y x) (-.f64 (.f64 z (/.f64 1 (-.f64 a t))) (/.f64 t (-.f64 a t)))))
40.0ms	(.f64 (-.f64 y x) (-.f64 (.f64 z (/.f64 1 (-.f64 a t))) (/.f64 t (-.f64 a t))))
8.0ms	(*.f64 z (/.f64 1 (-.f64 a t)))
6.0ms	(/.f64 t (-.f64 a t))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5188	2866

prune77.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	149	13	162

Merged error: 3.5b

Counts

162 → 13

Compiler

Compiled 3783 to 966 computations (74.5% saved)

regimes720.0ms (11.3%)

Compiler: Compiled 1512 to 1086 computations (28.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	123
1	93	123

end0.0ms (0%)

sample2.6s (41%)

Algorithm

1×

intervals

Results

291.0ms	6533×	body	80	valid
94.0ms	504×	body	640	valid
58.0ms	1197×	body	80	invalid
55.0ms	261×	body	1280	valid
54.0ms	401×	body	320	valid
23.0ms	278×	body	160	valid
6.0ms	23×	body	2560	valid

Compiler

Compiled 389 to 244 computations (37.3% saved)

Details

analyze1.3s (20.1%)

sample28.0ms (0.4%)

simplify97.0ms (1.5%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

rewrite35.0ms (0.6%)

series103.0ms (1.6%)

simplify77.0ms (1.2%)

prune104.0ms (1.6%)

localize9.0ms (0.1%)

rewrite36.0ms (0.6%)

series146.0ms (2.3%)

simplify134.0ms (2.1%)

prune163.0ms (2.6%)

localize10.0ms (0.2%)

rewrite111.0ms (1.7%)

series119.0ms (1.9%)

simplify103.0ms (1.6%)

prune126.0ms (2%)

localize12.0ms (0.2%)

rewrite51.0ms (0.8%)

series112.0ms (1.8%)

simplify86.0ms (1.3%)

prune77.0ms (1.2%)

regimes720.0ms (11.3%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.6s (41%)

Profiling