Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

sample224.0ms

Algorithm

intervals

Results

150.0ms	88×	body	2560	valid
46.0ms	92×	body	1280	valid
9.0ms	44×	body	640	valid
9.0ms	256×	pre	80	true
3.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	220	8
1	220	8

prune2.0ms

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: 60.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1.0 (tan.f64 x))
2.9b	(-.f64 (/.f64 1.0 x) (/.f64 1.0 (tan.f64 x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `div-inv_binary64`
2×	`pow1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(/.f64 1.0 (tan.f64 x))
13.0ms	(-.f64 (/.f64 1.0 x) (/.f64 1.0 (tan.f64 x)))

series40.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(/.f64 1.0 (tan.f64 x))
24.0ms	(-.f64 (/.f64 1.0 x) (/.f64 1.0 (tan.f64 x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4916	556
1	4916	556

prune63.0ms

Filtered

45 candidates to 55 candidates (-22.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	1	56

Merged error: 0.3b

Counts

56 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (*.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (*.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))

0.1b

(*.f64 0.0021164021164021165 (pow.f64 x 5))

0.1b

(*.f64 0.022222222222222223 (pow.f64 x 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`associate-l_binary64` `prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

3 → 69

Calls

3 calls:

9.0ms

(+.f64 (*.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (*.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))

5.0ms

(*.f64 0.0021164021164021165 (pow.f64 x 5))

6.0ms

(*.f64 0.022222222222222223 (pow.f64 x 3))

series21.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms

(+.f64 (*.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (*.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))

6.0ms

(*.f64 0.0021164021164021165 (pow.f64 x 5))

5.0ms

(*.f64 0.022222222222222223 (pow.f64 x 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4943	707
1	4943	707

prune83.0ms

Filtered

49 candidates to 78 candidates (-59.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Merged error: 0.2b

Counts

79 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))) (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
0.6b	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
0.6b	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
0.6b	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

20.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))) (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
8.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
8.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
11.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))) (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
28.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
24.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
26.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))

simplify42.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4987	3186
1	4987	3186

prune323.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	91	14	105

Merged error: 0.1b

Counts

105 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
0.6b	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
0.6b	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
0.6b	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod_binary64`
14×	`cbrt-div_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 61

Calls

4 calls:

8.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
9.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
11.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
9.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
31.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
28.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))
29.0ms	(cbrt.f64 (cbrt.f64 (+.f64 (.f64 0.022222222222222223 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021165 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))))

simplify35.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5554	2389

prune410.0ms

Filtered

69 candidates to 73 candidates (-5.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	72	15	87

Merged error: 0.1b

Counts

87 → 15

regimes90.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.4s

Algorithm

intervals

Results

5.5s	3235×	body	2560	valid
1.3s	2566×	body	1280	valid
249.0ms	1250×	body	640	valid
132.0ms	8000×	pre	80	true
68.0ms	577×	body	320	valid
27.0ms	322×	body	160	valid
2.0ms	50×	body	80	valid

Details

analyze6.0ms

sample224.0ms

simplify13.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series40.0ms

simplify50.0ms

prune63.0ms

localize9.0ms

rewrite22.0ms

series21.0ms

simplify58.0ms

prune83.0ms

localize15.0ms

rewrite49.0ms

series108.0ms

simplify42.0ms

prune323.0ms

localize20.0ms

rewrite38.0ms

series113.0ms

simplify35.0ms

prune410.0ms

regimes90.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling