Details

analyze1.1s (21.8%)

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%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	209×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	57×	body	80	invalid
1.0ms	7×	body	1280	valid
1.0ms	13×	body	160	valid
1.0ms	9×	body	320	valid

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

prune12.0ms (0.2%)

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: 12.2b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
3.0b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
3.6b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

rewrite37.0ms (0.8%)

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:

19.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
9.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

series124.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

64.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
43.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
17.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5183	1602

prune215.0ms (4.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	112	16	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	17	129

Merged error: 4.6b

Counts

129 → 17

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 a z))
0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
3.0b	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
5.1b	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
32×	`add-exp-log_binary64` `times-frac_binary64`
25×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64` `frac-times_binary64`
17×	`flip3--_binary64` `flip--_binary64`
13×	`prod-exp_binary64`
12×	`pow1_binary64`
10×	`associate-r/_binary64` `associate-l_binary64` `associate-l/_binary64`
9×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cbrt-unprod_binary64`
6×	`add-log-exp_binary64` `div-exp_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `un-div-inv_binary64`
3×	`1-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 146

Calls

4 calls:

18.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
15.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
6.0ms	(/.f64 1 (-.f64 a z))
5.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))

series135.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
46.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
16.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
6.0ms	(/.f64 1 (-.f64 a z))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5717	1769

prune214.0ms (4.4%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	2	13	15
Picked	0	1	1
Done	0	1	1
Total	158	17	175

Merged error: 4.6b

Counts

175 → 17

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
4.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
4.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
8.0b	(+.f64 x (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
93×	`cbrt-prod_binary64`
75×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-div_binary64` `flip3--_binary64` `pow1/3_binary64` `div-inv_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 131

Calls

4 calls:

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

series238.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))
58.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
57.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
56.0ms	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4933	2311
1	4933	2311

prune195.0ms (4%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	142	18	160

Merged error: 4.6b

Counts

160 → 18

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 y z))
1.6b	(*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z)))
1.7b	(.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z))))
8.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z)))))

rewrite66.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`cbrt-div_binary64`
84×	`frac-times_binary64`
58×	`flip3--_binary64` `flip--_binary64`
52×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
37×	`associate-*r/_binary64`
32×	`associate-l_binary64`
30×	`add-exp-log_binary64` `associate-*l/_binary64`
27×	`times-frac_binary64`
18×	`pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `cbrt-prod_binary64`
9×	`pow-prod-down_binary64` `associate-r_binary64`
6×	`add-log-exp_binary64`
4×	`unswap-sqr_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/r/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/3_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 166

Calls

4 calls:

27.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z))))
21.0ms	(*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z)))
5.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z)))))
3.0ms	(cbrt.f64 (-.f64 y z))

series217.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z)))
65.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z)))))
44.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (/.f64 (-.f64 t x) (-.f64 a z)) (cbrt.f64 (-.f64 y z))))
28.0ms	(cbrt.f64 (-.f64 y z))

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5157	3793

prune180.0ms (3.7%)

Pruning

19 alts after pruning (15 fresh and 4 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	14	14
Picked	0	1	1
Done	0	3	3
Total	177	19	196

Merged error: 4.2b

Counts

196 → 19

regimes873.0ms (18.1%)

Accuracy

Total 6.0b remaining (66.1%)

Threshold costs 0b (0%)

bsearch4.0ms (0.1%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	57
1	64	57

end0.0ms (0%)

sample798.0ms (16.5%)

Algorithm

1×

intervals

Results

274.0ms	6569×	body	80	valid
68.0ms	479×	body	640	valid
47.0ms	407×	body	320	valid
45.0ms	250×	body	1280	valid
44.0ms	1157×	body	80	invalid
21.0ms	280×	body	160	valid
3.0ms	15×	body	2560	valid

Details

analyze1.1s (21.8%)

sample30.0ms (0.6%)

simplify81.0ms (1.7%)

prune12.0ms (0.2%)

localize9.0ms (0.2%)

rewrite37.0ms (0.8%)

series124.0ms (2.6%)

simplify46.0ms (1%)

prune215.0ms (4.4%)

localize10.0ms (0.2%)

rewrite51.0ms (1%)

series135.0ms (2.8%)

simplify55.0ms (1.1%)

prune214.0ms (4.4%)

localize13.0ms (0.3%)

rewrite35.0ms (0.7%)

series238.0ms (4.9%)

simplify79.0ms (1.6%)

prune195.0ms (4%)

localize13.0ms (0.3%)

rewrite66.0ms (1.4%)

series217.0ms (4.5%)

simplify48.0ms (1%)

prune180.0ms (3.7%)

regimes873.0ms (18.1%)

bsearch4.0ms (0.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample798.0ms (16.5%)

Profiling