Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample243.0ms

Algorithm

intervals

Results

142.0ms	58×	body	2560	valid
62.0ms	87×	body	1280	valid
15.0ms	55×	body	640	valid
9.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid
2.0ms	19×	body	80	valid

simplify495.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune4.0ms

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: 31.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.8b	(-.f64 x (sin.f64 x))
1.0b	(-.f64 x (tan.f64 x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (tan.f64 x))

series43.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (sin.f64 x))
24.0ms	(-.f64 x (tan.f64 x))

simplify75.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune80.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.3b	(*.f64 27/2800 (pow.f64 x 4))
13.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms	(.f64 (.f64 x x) 9/40)
5.0ms	(*.f64 27/2800 (pow.f64 x 4))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

series16.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(.f64 (.f64 x x) 9/40)
5.0ms	(*.f64 27/2800 (pow.f64 x 4))
7.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

simplify31.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4961	578
1	4961	578

prune61.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	65	5	70

Merged error: 0.0b

Counts

70 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

13.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
15.3b	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
15.3b	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
15.3b	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp_binary64` `cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/3_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `sum-log_binary64`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
9.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
9.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
9.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
19.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
16.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
18.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5904	1358

prune148.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	64	5	69

Merged error: 0.0b

Counts

69 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

15.3b	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
15.3b	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
22.9b	(/.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) 3))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) 81/1600) (.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2))))))
25.4b	(-.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod_binary64`
36×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`cbrt-div_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `associate-/l_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 101

Calls

4 calls:

9.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
9.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
17.0ms	(/.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) 3))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) 81/1600) (.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2))))))
10.0ms	(-.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) 3))

series75.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
15.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2)))
28.0ms	(/.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) 3))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) 81/1600) (.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2))))))
17.0ms	(-.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 (.f64 27/2800 (pow.f64 x 4)) 1/2) 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5006	5844

prune744.0ms

Filtered

105 candidates to 113 candidates (-7.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	113	5	118

Merged error: 0.0b

Counts

118 → 5

regimes81.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch37.0ms

Steps

Iters	Range		Point
8	0.014178460367165312	142.67258068776127	0.02856113453362911
10	-86.26200852349665	-2.2673774106756e-10	-0.02779748745899354

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	31
1	86	31

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.9s	1603×	body	2560	valid
1.7s	2739×	body	1280	valid
510.0ms	1882×	body	640	valid
171.0ms	972×	body	320	valid
61.0ms	477×	body	160	valid
25.0ms	327×	body	80	valid

Details

analyze1.2s

sample243.0ms

simplify495.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series43.0ms

simplify75.0ms

prune80.0ms

localize9.0ms

rewrite22.0ms

series16.0ms

simplify31.0ms

prune61.0ms

localize15.0ms

rewrite38.0ms

series59.0ms

simplify43.0ms

prune148.0ms

localize29.0ms

rewrite49.0ms

series75.0ms

simplify70.0ms

prune744.0ms

regimes81.0ms

bsearch37.0ms

simplify3.0ms

end0.0ms

sample6.5s

Profiling