Details

Time bar (total: 6.7s)

sample95.0ms

Algorithm
intervals
Results
48.0ms137×body1280valid
21.0ms25×body2560valid
13.0ms62×body640valid
3.0ms19×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: 37.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
3.7b
(cos (+ x eps))

rewrite13.0ms

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:
7.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

series70.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify75.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune119.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
0.2b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
1.2b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

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:
5.0ms
(* (cos x) (cos eps))
5.0ms
(* (sin x) (sin eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
10.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series301.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos x) (cos eps))
45.0ms
(* (sin x) (sin eps))
83.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
130.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0381988
11342837
25001822

prune310.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.1b
(fma (sin x) (sin eps) (cos x))
1.3b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
1.3b
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

rewrite7.0ms

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:
2.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
1.0ms
(fma (sin x) (sin eps) (cos x))
1.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
2.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
55.0ms
(fma (sin x) (sin eps) (cos x))
135.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
144.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0137627
1357554
21340554
35002551

prune268.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.1b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
145×prod-diff
110×add-sqr-sqrt
98×*-un-lft-identity
93×unpow-prod-down cube-prod
86×add-cube-cbrt
35×sqr-pow
27×cube-mult unpow3
16×difference-of-squares
12×fma-neg
11×add-log-exp
6×pow1 add-exp-log pow-unpow add-cbrt-cube
5×distribute-lft-out--
4×cube-div expm1-log1p-u log1p-expm1-u
3×associate-+l+ fma-def
2×pow-to-exp sub-neg flip3-- pow-pow diff-log pow-exp sum-log cos-mult flip-- sin-mult rem-cube-cbrt
1×difference-cubes +-commutative associate-+l- flip3-+ frac-sub flip-+ distribute-lft-out sub-div
Counts
4 → 268
Calls
4 calls:
3.0ms
(pow (cos x) 3)
10.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
9.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
22.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series841.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (cos x) 3)
99.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
107.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
605.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify167.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
08745051
137823725
250013720

prune509.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.3b

regimes260.0ms

Accuracy

86.7% (1.3b remaining)

Error of 15.1b against oracle of 13.8b and baseline of 23.8b

bsearch130.0ms

Steps
ItersRangePoint
9
4.808780483129348e-13
8.07893749493944e-05
2.6734197226084376e-08
9
-0.00013776134412608358
-1.1851374698435839e-09
-2.1400263784195043e-07

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04551
14751
24751

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4441×body1280valid
564.0ms636×body2560valid
376.0ms1830×body640valid
111.0ms701×body320valid
30.0ms304×body160valid
4.0ms88×body80valid