Details

Time bar (total: 6.0s)

sample125.0ms

Algorithm
intervals
Results
55.0ms42×body2560valid
39.0ms90×body1280valid
16.0ms68×body640valid
5.0ms31×body320valid
2.0ms15×body160valid
1.0ms10×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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))

series62.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify81.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune161.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New441458
Fresh000
Picked101
Done000
Total451459

Merged error: 0.2b

Counts
59 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (sin x))
0.2b
(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.0b
(- 1.0 (cos x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
20×times-frac
19×add-cube-cbrt
16×add-exp-log
13×associate-*r*
10×add-cbrt-cube
6×pow1
5×associate-*l* add-log-exp
4×div-exp prod-exp
3×flip3-- associate-/r* flip-- associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
3 → 87
Calls
3 calls:
4.0ms
(/ 1 (sin x))
13.0ms
(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms
(- 1.0 (cos x))

series67.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ 1 (sin x))
35.0ms
(* (- 1.0 (cos x)) (/ 1 (sin x)))
19.0ms
(- 1.0 (cos x))

simplify47.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0320546
11393480
25001454

prune153.0ms

Filtered
96 candidates to 54 candidates (56.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New93396
Fresh4913
Picked011
Done000
Total9713110

Merged error: 0.2b

Counts
110 → 13

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sin x))
0.2b
(/ (cos x) (sin x))
1.1b
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
28×times-frac
21×add-cube-cbrt
7×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
5×add-log-exp
4×div-inv distribute-lft-out-- difference-of-squares
3×pow1
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 77
Calls
3 calls:
3.0ms
(/ 1.0 (sin x))
4.0ms
(/ (cos x) (sin x))
13.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series129.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(/ 1.0 (sin x))
19.0ms
(/ (cos x) (sin x))
87.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify61.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0287581
1772552
22215552
35002551

prune188.0ms

Filtered
86 candidates to 67 candidates (77.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New82486
Fresh2911
Picked101
Done101
Total861399

Merged error: 0.1b

Counts
99 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (sin x))
0.1b
(/ 1.0 (sin x))
0.2b
(* (cos x) (/ 1 (sin x)))
1.1b
(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
29×*-un-lft-identity times-frac
28×add-cube-cbrt
19×add-exp-log
13×associate-*r* add-cbrt-cube
7×pow1
6×associate-/r* associate-/l* add-log-exp
5×div-exp
4×prod-exp div-inv
3×cbrt-undiv associate-*r/ associate-*l* un-div-inv unswap-sqr
2×rec-exp frac-2neg 1-exp clear-num frac-sub cbrt-unprod sub-div
1×sub-neg flip3-- distribute-rgt-out-- pow-flip diff-log pow-prod-down *-commutative flip-- inv-pow
Counts
4 → 111
Calls
4 calls:
7.0ms
(/ 1 (sin x))
3.0ms
(/ 1.0 (sin x))
8.0ms
(* (cos x) (/ 1 (sin x)))
7.0ms
(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

series138.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1 (sin x))
19.0ms
(/ 1.0 (sin x))
19.0ms
(* (cos x) (/ 1 (sin x)))
87.0ms
(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

simplify98.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
0391699
11433625
24811579
35001575

prune182.0ms

Filtered
123 candidates to 78 candidates (63.4%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1221123
Fresh01212
Picked011
Done000
Total12214136

Merged error: 0.1b

Counts
136 → 14

regimes147.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 30.2b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04128
14128

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1570×body2560valid
1.2s2750×body1280valid
472.0ms1924×body640valid
155.0ms919×body320valid
54.0ms471×body160valid
25.0ms362×body80valid
22.0ms4×body5120valid

Profiling

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