Details

analyze107.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

sample23.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
0.0ms	1×	body	80	nan

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4987	40
1	4987	40

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-r_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)
18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
13.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(.f64 5 (.f64 v v))
13.0ms	(*.f64 PI.f64 t)
171.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
98.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5648	2775

prune159.0ms

Filtered

74 candidates to 106 candidates (-43.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.1b

Counts

107 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 5)
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (pow.f64 v 4))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
7×	`pow-prod-down_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 5)
4.0ms	(*.f64 PI.f64 t)
21.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (pow.f64 v 4))))
11.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(.f64 (.f64 v v) 5)
14.0ms	(*.f64 PI.f64 t)
166.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (pow.f64 v 4))))
97.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4972	2805
1	4972	2805

prune165.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Merged error: 0.1b

Counts

117 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
0.4b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

30×	`associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
9×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
8×	`associate-/r/_binary64`
7×	`pow-prod-down_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(.f64 5 (.f64 v v))
18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
11.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
8.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(.f64 5 (.f64 v v))
172.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
99.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
89.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5002	3124

prune157.0ms

Filtered

81 candidates to 108 candidates (-33.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	109	10	119

Merged error: 0.1b

Counts

119 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 t)
0.3b	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
0.3b	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

368×	`associate-*r/_binary64`
228×	`cbrt-div_binary64` `sqrt-div_binary64`
168×	`frac-times_binary64`
142×	`flip3--_binary64` `flip--_binary64`
84×	`associate-*l/_binary64`
80×	`associate-/r/_binary64`
69×	`add-exp-log_binary64`
47×	`add-cbrt-cube_binary64`
41×	`cbrt-unprod_binary64` `prod-exp_binary64`
36×	`pow1_binary64`
22×	`pow-prod-down_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-prod_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64`
1×	`associate-/r*_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 219

Calls

4 calls:

4.0ms	(*.f64 PI.f64 t)
22.0ms	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
34.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
13.0ms	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(*.f64 PI.f64 t)
102.0ms	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
174.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
236.0ms	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))

simplify163.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4990	13910
1	4990	13910

prune929.0ms

Filtered

169 candidates to 231 candidates (-36.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	226	5	231
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	229	12	241

Merged error: 0.1b

Counts

241 → 12

regimes171.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms

sample656.0ms

Algorithm

intervals

Results

512.0ms	8000×	body	80	valid
1.0ms	11×	body	80	nan

Details

analyze107.0ms

sample23.0ms

simplify63.0ms

prune5.0ms

localize16.0ms

rewrite43.0ms

series300.0ms

simplify71.0ms

prune159.0ms

localize19.0ms

rewrite45.0ms

series295.0ms

simplify72.0ms

prune165.0ms

localize16.0ms

rewrite49.0ms

series379.0ms

simplify89.0ms

prune157.0ms

localize20.0ms

rewrite99.0ms

series525.0ms

simplify163.0ms

prune929.0ms

regimes171.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample656.0ms

Profiling