Details

analyze5.0ms

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

sample232.0ms

Algorithm

intervals

Results

163.0ms	97×	body	2560	valid
49.0ms	92×	body	1280	valid
8.0ms	43×	body	640	valid
4.0ms	256×	pre	80	true
1.0ms	13×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	8
1	71	8

prune1.0ms

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: 60.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
2.6b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-exp-log_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

2 → 60

Calls

2 calls:

4.0ms	(/.f64 1 (tan.f64 x))
14.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series25.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/.f64 1 (tan.f64 x))
15.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4848	639
1	4848	639

prune39.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	1	67

Merged error: 0.3b

Counts

67 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.3b	(*.f64 x 1/3)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

9.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
6.0ms	(*.f64 1/45 (pow.f64 x 3))
7.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 x 1/3)

series18.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
4.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
2.0ms	(*.f64 x 1/3)

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5108	791

prune73.0ms

Filtered

64 candidates to 99 candidates (-54.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	6	100

Merged error: 0.2b

Counts

100 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/45))
0.1b	(*.f64 (pow.f64 x 3) 1/45)
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.3b	(*.f64 x 1/3)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

5.0ms	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/45))
6.0ms	(*.f64 (pow.f64 x 3) 1/45)
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 x 1/3)

series24.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/45))
4.0ms	(*.f64 (pow.f64 x 3) 1/45)
5.0ms	(*.f64 2/945 (pow.f64 x 5))
2.0ms	(*.f64 x 1/3)

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5080	693

prune64.0ms

Filtered

62 candidates to 97 candidates (-56.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 0.2b

Counts

103 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_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`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series62.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
16.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4940	374
1	4940	374

prune60.0ms

Filtered

65 candidates to 85 candidates (-30.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	79	12	91

Merged error: 0.1b

Counts

91 → 12

regimes39.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.2s

Algorithm

intervals

Results

5.2s	3255×	body	2560	valid
1.3s	2497×	body	1280	valid
227.0ms	1246×	body	640	valid
134.0ms	8000×	pre	80	true
72.0ms	625×	body	320	valid
26.0ms	319×	body	160	valid
2.0ms	58×	body	80	valid

Details

analyze5.0ms

sample232.0ms

simplify7.0ms

prune1.0ms

localize5.0ms

rewrite21.0ms

series25.0ms

simplify60.0ms

prune39.0ms

localize9.0ms

rewrite29.0ms

series18.0ms

simplify50.0ms

prune73.0ms

localize9.0ms

rewrite23.0ms

series24.0ms

simplify49.0ms

prune64.0ms

localize13.0ms

rewrite12.0ms

series62.0ms

simplify57.0ms

prune60.0ms

regimes39.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.2s

Profiling