Details

Time bar (total: 7.3s)

sample95.0ms

Algorithm
intervals
Results
49.0ms133×body1280valid
17.0ms19×body2560valid
15.0ms68×body640valid
4.0ms23×body320valid
1.0ms9×body160valid
0.0ms4×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
3.2b
(cos (+ x eps))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
7.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series68.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(- (cos (+ x eps)) (cos x))
20.0ms
(cos (+ x eps))

simplify111.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune96.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
3.1b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sub-neg cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 70
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms
(* (sin x) (sin eps))
20.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series284.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos x) (cos eps))
78.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms
(* (sin x) (sin eps))
122.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify110.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune234.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b
(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
3.8b
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1
34×pow-prod-down
30×add-exp-log add-cbrt-cube
23×cos-mult sin-mult
18×add-sqr-sqrt
16×prod-exp cbrt-unprod associate-/l/
15×*-un-lft-identity
13×add-cube-cbrt times-frac
12×associate-*r/ associate-*l/
10×frac-times
9×frac-sub
8×pow-sqr pow-prod-up
6×add-log-exp difference-of-squares
5×sub-div
4×pow-plus associate-/l*
3×associate-/r* associate-/r/
2×pow2 flip3-- div-sub swap-sqr associate-*r* associate-*l* *-commutative flip--
1×cbrt-undiv associate--l- sub-neg frac-2neg flip3-+ diff-log div-exp frac-add clear-num flip-+ div-inv distribute-lft-out--
Counts
4 → 141
Calls
4 calls:
14.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
13.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
47.0ms
(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
117.0ms
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series651.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
51.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
197.0ms
(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
351.0ms
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify94.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06202413
132092129
250012123

prune495.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 14.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b
(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* 1 (* (* (sin x) (sin eps)) (* (sin x) (sin eps))))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
3.8b
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* 1 (* (* (sin x) (sin eps)) (* (sin x) (sin eps))))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1
34×pow-prod-down
30×add-exp-log add-cbrt-cube
26×associate-*r/
23×cos-mult sin-mult
17×add-sqr-sqrt
16×prod-exp cbrt-unprod associate-/l/
14×*-un-lft-identity
12×add-cube-cbrt associate-*l/
10×frac-times times-frac
9×frac-sub
8×pow-sqr pow-prod-up
6×add-log-exp
5×sub-div
4×pow-plus
3×associate-/r* associate-/r/ associate-/l*
2×pow2 flip3-- div-sub swap-sqr associate-*r* associate-*l* *-commutative flip-- difference-of-squares
1×cbrt-undiv associate--l- sub-neg frac-2neg flip3-+ diff-log div-exp frac-add clear-num flip-+ div-inv distribute-lft-out--
Counts
4 → 137
Calls
4 calls:
14.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
13.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
55.0ms
(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* 1 (* (* (sin x) (sin eps)) (* (sin x) (sin eps))))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
114.0ms
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* 1 (* (* (sin x) (sin eps)) (* (sin x) (sin eps))))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series651.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
53.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
195.0ms
(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* 1 (* (* (sin x) (sin eps)) (* (sin x) (sin eps))))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
353.0ms
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* 1 (* (* (sin x) (sin eps)) (* (sin x) (sin eps))))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify104.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06162388
132852053
250012047

prune406.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.8b

regimes247.0ms

Accuracy

81.5% (1.9b remaining)

Error of 16.0b against oracle of 14.1b and baseline of 24.3b

bsearch125.0ms

Steps
ItersRangePoint
8
1.7051359805205634e-09
2.9691085793320403e-05
1.0478829995291909e-07
9
-2.407089977546517e-20
-1.9686181127470131e-25
-2.384759822263193e-20

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04443
14443

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s4387×body1280valid
573.0ms648×body2560valid
433.0ms1848×body640valid
123.0ms718×body320valid
39.0ms316×body160valid
6.0ms83×body80valid