Details

sample135.0ms

Algorithm

intervals

Results

64.0ms	49×	body	2560	valid
38.0ms	83×	body	1280	valid
15.0ms	58×	body	640	valid
7.0ms	36×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	14×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.5b	(- 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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

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

prune161.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

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)))
0.1b	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite23.0ms

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:

9.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
7.0ms	(* 1/24 (pow x 3))
6.0ms	(* 1/240 (pow x 5))

series146.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
35.0ms	(* 1/24 (pow x 3))
50.0ms	(* 1/240 (pow x 5))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5001	346

prune186.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) (- 1.0 (cos x)))
0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
2.5b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

10.0ms	(/ (sin x) (- 1.0 (cos x)))
10.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series91.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin x) (- 1.0 (cos x)))
33.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	510	1595
1	2396	1452
2	5002	1339

prune241.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (log (exp (- 1.0 (cos x)))))
0.1b	(/ 1 (/ (sin x) (log (exp (- 1.0 (cos x))))))
2.5b	(- 1.0 (cos x))
2.6b	(log (exp (- 1.0 (cos x))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

228×	`times-frac`
156×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`add-cube-cbrt`
102×	`log-pow`
85×	`exp-prod`
40×	`associate-/r*`
22×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`log-prod`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `exp-sum` `clear-num`
1×	`log-div` `flip3--` `pow-flip` `exp-diff` `diff-log` `rem-log-exp` `associate-/r/` `flip--` `inv-pow`

Counts

4 → 233

Calls

4 calls:

16.0ms	(/ (sin x) (log (exp (- 1.0 (cos x)))))
22.0ms	(/ 1 (/ (sin x) (log (exp (- 1.0 (cos x))))))
3.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (- 1.0 (cos x))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sin x) (log (exp (- 1.0 (cos x)))))
39.0ms	(/ 1 (/ (sin x) (log (exp (- 1.0 (cos x))))))
17.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify76.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	668	2478
1	2830	2139
2	5001	1963

prune342.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes62.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.5b

bsearch88.0ms

Steps

Iters	Range		Point
9	0.00035723662727133143	33.11368705657117	0.022419207862011653
10	-29.541817090935037	-6.322351620237733e-11	-0.018610874840414206

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	1614×	body	2560	valid
1.3s	2733×	body	1280	valid
497.0ms	1883×	body	640	valid
170.0ms	950×	body	320	valid
59.0ms	460×	body	160	valid
34.0ms	353×	body	80	valid
29.0ms	7×	body	5120	valid