Details

analyze114.0ms

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

sample24.0ms

Algorithm

intervals

Results

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

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5222	28

prune6.0ms

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: 0.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 3.0 (.f64 v v))
0.3b	(*.f64 PI.f64 t)
0.5b	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (-.f64 1.0 (*.f64 v v))))
0.5b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v))))))

rewrite42.0ms

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 3.0 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)
19.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (-.f64 1.0 (*.f64 v v))))
10.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v))))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 3.0 (.f64 v v))
3.0ms	(*.f64 PI.f64 t)
52.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (-.f64 1.0 (*.f64 v v))))
25.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5017	1908

prune155.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	9	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 0.3b

Counts

107 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 5.0 (.f64 v v))
0.3b	(*.f64 PI.f64 t)
0.5b	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 (.f64 3.0 v) v))))) (-.f64 1.0 (*.f64 v v))))
0.5b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 (*.f64 3.0 v) v)))))

rewrite42.0ms

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 5.0 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)
17.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 (.f64 3.0 v) v))))) (-.f64 1.0 (*.f64 v v))))
13.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 (*.f64 3.0 v) v)))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 5.0 (.f64 v v))
3.0ms	(*.f64 PI.f64 t)
53.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 (.f64 3.0 v) v))))) (-.f64 1.0 (*.f64 v v))))
25.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 (*.f64 3.0 v) v)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5018	1908

prune140.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Merged error: 0.3b

Counts

115 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 3.0 (.f64 v v))
0.4b	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v)))))))
0.4b	(.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))
0.5b	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))) (-.f64 1.0 (*.f64 v v))))

rewrite46.0ms

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 3.0 (.f64 v v))
10.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v)))))))
8.0ms	(.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))
17.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))) (-.f64 1.0 (*.f64 v v))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 3.0 (.f64 v v))
24.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v)))))))
24.0ms	(.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))
49.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))) (-.f64 1.0 (*.f64 v v))))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5000	2144

prune166.0ms

Filtered

82 candidates to 108 candidates (-31.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	106	11	117

Merged error: 0.3b

Counts

117 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v))))))))
0.3b	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v)))))))
0.3b	(*.f64 PI.f64 t)
0.5b	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))) (-.f64 1.0 (*.f64 v v))))

rewrite92.0ms

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:

17.0ms	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v))))))))
17.0ms	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v)))))))
4.0ms	(*.f64 PI.f64 t)
31.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))) (-.f64 1.0 (*.f64 v v))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v))))))))
26.0ms	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (*.f64 v v)))))))
3.0ms	(*.f64 PI.f64 t)
55.0ms	(/.f64 (-.f64 1.0 (.f64 5.0 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2.0 (-.f64 1.0 (.f64 3.0 (.f64 v v))))))) (-.f64 1.0 (*.f64 v v))))

simplify69.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5720	9994

prune773.0ms

Filtered

170 candidates to 231 candidates (-35.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	233	9	242

Merged error: 0.2b

Counts

242 → 9

regimes285.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	28
1	91	28

end0.0ms

sample664.0ms

Algorithm

intervals

Results

525.0ms	8000×	body	80	valid
1.0ms	9×	body	80	nan

Details

analyze114.0ms

sample24.0ms

simplify35.0ms

prune6.0ms

localize15.0ms

rewrite42.0ms

series84.0ms

simplify67.0ms

prune155.0ms

localize16.0ms

rewrite42.0ms

series86.0ms

simplify53.0ms

prune140.0ms

localize15.0ms

rewrite46.0ms

series101.0ms

simplify54.0ms

prune166.0ms

localize22.0ms

rewrite92.0ms

series346.0ms

simplify69.0ms

prune773.0ms

regimes285.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample664.0ms

Profiling