Details

Time bar (total: 6.1s)

sample140.0ms

Algorithm
intervals
Results
76.0ms57×body2560valid
35.0ms83×body1280valid
16.0ms73×body640valid
4.0ms24×body320valid
1.0ms12×body160valid
0.0ms7×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.2b
(- 1.0 (cos x))

rewrite13.0ms

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))

series61.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ (- 1.0 (cos x)) (sin x))
25.0ms
(- 1.0 (cos x))

simplify80.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune156.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 1/240 (pow x 5))
0.3b
(* 1/24 (pow x 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×associate-*r*
12×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×unswap-sqr
6×associate-*l* prod-exp add-cbrt-cube
4×cube-prod sqr-pow
2×pow1 pow-to-exp pow-exp *-commutative cbrt-unprod add-log-exp
1×cube-mult unpow3
Counts
2 → 56
Calls
2 calls:
5.0ms
(* 1/240 (pow x 5))
7.0ms
(* 1/24 (pow x 3))

series89.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(* 1/240 (pow x 5))
37.0ms
(* 1/24 (pow x 3))

simplify185.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0208209
1871193
24634193
35001193

prune147.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin x) (- 1.0 (cos x)))
0.2b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
1.2b
(- 1.0 (cos x))

rewrite27.0ms

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:
6.0ms
(/ (sin x) (- 1.0 (cos x)))
10.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

series94.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ (sin x) (- 1.0 (cos x)))
40.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
18.0ms
(- 1.0 (cos x))

simplify60.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05101595
123961452
250011339

prune265.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin x) (- 1.0 (cos x)))
0.2b
(/ 1 (pow (/ (sin x) (- 1.0 (cos x))) 1))
1.2b
(- 1.0 (cos x))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
113×add-sqr-sqrt *-un-lft-identity
84×unpow-prod-down
79×add-cube-cbrt
30×associate-/r*
21×add-exp-log
17×distribute-lft-out-- difference-of-squares
12×div-exp
10×associate-/r/
7×add-cbrt-cube
6×flip3-- pow-exp flip-- div-inv associate-/l*
5×add-log-exp
4×rec-exp 1-exp sqr-pow
3×pow1 pow-to-exp
2×cbrt-undiv frac-2neg clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 179
Calls
3 calls:
7.0ms
(/ (sin x) (- 1.0 (cos x)))
19.0ms
(/ 1 (pow (/ (sin x) (- 1.0 (cos x))) 1))
3.0ms
(- 1.0 (cos x))

series96.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ (sin x) (- 1.0 (cos x)))
41.0ms
(/ 1 (pow (/ (sin x) (- 1.0 (cos x))) 1))
19.0ms
(- 1.0 (cos x))

simplify66.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05581959
125981644
250011521

prune283.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes111.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.6b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03727
13727

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.1s1656×body2560valid
1.2s2763×body1280valid
419.0ms1843×body640valid
135.0ms921×body320valid
53.0ms448×body160valid
22.0ms365×body80valid
16.0ms4×body5120valid