Details

sample122.0ms

Algorithm

intervals

Results

55.0ms	48×	body	2560	valid
38.0ms	90×	body	1280	valid
14.0ms	66×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	8×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.9b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify82.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune167.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	41	17	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	17	59

Merged error: 0.1b

Counts

59 → 17

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.0b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

7.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series149.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
47.0ms	(* 1/240 (pow x 5))
40.0ms	(* 1/24 (pow x 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5002	346

prune175.0ms

Filtered

78 candidates to 49 candidates (62.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	78	17	95

Merged error: 0.1b

Counts

95 → 17

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.2b	(- 1.0 (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
4.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series153.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
76.0ms	(log (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify85.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	289	829
1	791	761
2	2667	734
3	5001	708

prune218.0ms

Filtered

110 candidates to 65 candidates (59.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	111	16	127

Merged error: 0.1b

Counts

127 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.2b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune248.0ms

Filtered

124 candidates to 88 candidates (71.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	121	19	140

Merged error: 0.1b

Counts

140 → 19

regimes200.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.8b

bsearch75.0ms

Steps

Iters	Range		Point
7	0.00999808388340962	0.475758948552502	0.024621020206448203
9	-164485.30314980465	-0.009598081335721272	-0.023734893863066063

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	28
1	45	28

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.2s	1616×	body	2560	valid
1.2s	2725×	body	1280	valid
639.0ms	1917×	body	640	valid
144.0ms	946×	body	320	valid
46.0ms	429×	body	160	valid
24.0ms	5×	body	5120	valid
23.0ms	362×	body	80	valid