Details

Time bar (total: 5.8s)

sample141.0ms

Algorithm
intervals
Results
73.0ms54×body2560valid
36.0ms73×body1280valid
15.0ms64×body640valid
5.0ms35×body320valid
2.0ms15×body160valid
1.0ms15×body80valid

simplify5.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 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))
3.0ms
(- 1.0 (cos x))

series11.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify78.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune127.0ms

Filtered
58 candidates to 42 candidates (27.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New441458
Fresh000
Picked101
Done000
Total451459

Merged error: 0.2b

Counts
59 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×associate-*r*
3×pow-unpow associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 92
Calls
4 calls:
6.0ms
(* (cos x) (+ (cos x) 1.0))
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series20.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (cos x) (+ (cos x) 1.0))
5.0ms
(pow (cos x) 3)
2.0ms
(+ (cos x) 1.0)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0353593
11734555
25001535

prune182.0ms

Filtered
104 candidates to 61 candidates (41.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New977104
Fresh4913
Picked101
Done000
Total10216118

Merged error: 0.1b

Counts
118 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(pow (+ (cos x) 1.0) 3)
0.5b
(+ (cos x) 1.0)
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
26×*-un-lft-identity
19×unpow-prod-down cube-prod
16×difference-of-squares
10×add-cube-cbrt sqr-pow
8×add-log-exp
6×pow1 add-exp-log pow-unpow add-cbrt-cube
5×distribute-lft-out--
3×distribute-lft-out
2×cube-div cube-mult pow-to-exp pow-pow flip3-+ unpow3 pow-exp flip-+ rem-cube-cbrt
1×difference-cubes +-commutative sub-neg flip3-- diff-log sum-log flip--
Counts
4 → 96
Calls
4 calls:
2.0ms
(pow (cos x) 3)
5.0ms
(pow (+ (cos x) 1.0) 3)
4.0ms
(+ (cos x) 1.0)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series21.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos x) 3)
6.0ms
(pow (+ (cos x) 1.0) 3)
2.0ms
(+ (cos x) 1.0)
9.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify55.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0365582
11604552
25002528

prune200.0ms

Filtered
108 candidates to 59 candidates (45.4%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1062108
Fresh11415
Picked101
Done000
Total10816124

Merged error: 0.1b

Counts
124 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.8b
(- (pow 1.0 3) (pow (cos x) 3))
1.9b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
32×difference-of-squares
31×*-un-lft-identity
27×unpow-prod-down cube-prod
26×log-pow
25×exp-prod
17×sqr-pow
10×distribute-lft-out--
9×add-cube-cbrt
8×add-log-exp
6×pow1
5×add-exp-log log-prod add-cbrt-cube
3×pow-unpow
2×difference-cubes sub-neg exp-sum
1×+-commutative cube-mult pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log unpow3 rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 109
Calls
4 calls:
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))
14.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series21.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos x) 3)
2.0ms
(+ (cos x) 1.0)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))
7.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify49.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0348673
11242636
25001608

prune174.0ms

Filtered
121 candidates to 69 candidates (43.0%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1192121
Fresh01515
Picked101
Done000
Total12017137

Merged error: 0.1b

Counts
137 → 17

regimes199.0ms

Accuracy

97.8% (0.7b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.3b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05851
15851

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.1s1605×body2560valid
1.2s2801×body1280valid
463.0ms1896×body640valid
142.0ms865×body320valid
54.0ms466×body160valid
24.0ms366×body80valid
3.0ms1×body5120valid

Profiling

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