Details

Time bar (total: 5.4s)

sample84.0ms

Algorithm
intervals
Results
42.0ms136×body1280valid
14.0ms17×body2560valid
12.0ms64×body640valid
4.0ms31×body320valid
1.0ms8×body160valid

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: 39.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
2.7b
(cos (+ x eps))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u cos-sum add-cbrt-cube log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
20.0ms
(- (cos (+ x eps)) (cos x))
9.0ms
(cos (+ x eps))

series67.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune114.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
3.2b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×prod-diff add-log-exp
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-neg diff-log log1p-expm1-u
3×sub-neg associate--l+ cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 93
Calls
4 calls:
16.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
10.0ms
(* (cos x) (cos eps))
11.0ms
(* (sin x) (sin eps))
65.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series305.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
46.0ms
(* (cos x) (cos eps))
44.0ms
(* (sin x) (sin eps))
135.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify51.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0381989
11342838
25001822

prune283.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
3.2b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma (sin x) (sin eps) (cos x))
0.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series202.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(fma (sin x) (sin eps) (cos x))
142.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify119.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune144.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
0.1b
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
3.2b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
3.2b
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×pow1 add-log-exp
4×add-exp-log expm1-log1p-u log-prod log-pow add-cbrt-cube fma-udef log1p-expm1-u
2×exp-sum
1×rem-log-exp rem-exp-log
Counts
4 → 52
Calls
4 calls:
0.0ms
(fma (sin x) (sin eps) (cos x))
2.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
3.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(fma (sin x) (sin eps) (cos x))
145.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
139.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
146.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

simplify42.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
0137627
1357554
21340554
35002551

prune215.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

regimes177.0ms

Accuracy

87.7% (1.3b remaining)

Error of 15.6b against oracle of 14.4b and baseline of 24.8b

bsearch101.0ms

Steps
ItersRangePoint
6
5.214836503720958e-10
3.7141773282228235e-09
3.588703897944784e-09
9
-2.2082264187638084e-10
-1.8774124276059505e-19
-8.396995804045069e-12

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13720

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s4399×body1280valid
567.0ms660×body2560valid
371.0ms1881×body640valid
92.0ms692×body320valid
27.0ms283×body160valid
4.0ms85×body80valid