Details

Time bar (total: 6.3s)

sample94.0ms

Algorithm
intervals
Results
42.0ms128×body1280valid
26.0ms31×body2560valid
13.0ms63×body640valid
3.0ms22×body320valid
1.0ms10×body160valid
0.0ms2×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: 41.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
4.6b
(cos (+ x eps))

rewrite13.0ms

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))
5.0ms
(cos (+ x eps))

series66.0ms

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

simplify122.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune86.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.7b

localize16.0ms

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))
2.4b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite36.0ms

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)))
5.0ms
(* (sin x) (sin eps))
21.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series309.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos x) (cos eps))
86.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms
(* (sin x) (sin eps))
134.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify119.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune246.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
0.2b
(- (- (* (sin x) (sin eps))) (cos x))
2.3b
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×add-log-exp
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sum-log cos-mult
2×sub-neg associate-+r+ flip3-- pow-prod-down neg-log frac-add prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×+-commutative associate--l- neg-sub0 associate-+r- flip3-+ flip-+ sin-mult distribute-lft-out-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
7.0ms
(* (cos x) (cos eps))
4.0ms
(* (sin x) (sin eps))
6.0ms
(- (- (* (sin x) (sin eps))) (cos x))
14.0ms
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (cos x) (cos eps))
43.0ms
(* (sin x) (sin eps))
59.0ms
(- (- (* (sin x) (sin eps))) (cos x))
131.0ms
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0362707
11473662
25001640

prune273.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b
(pow (- (- (* (sin x) (sin eps))) (cos x)) 3)
0.5b
(pow (* (cos x) (cos eps)) 3)
2.2b
(+ (pow (* (cos x) (cos eps)) 3) (pow (- (- (* (sin x) (sin eps))) (cos x)) 3))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
20×add-exp-log add-cbrt-cube
18×pow-prod-down
14×*-un-lft-identity
12×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-cube-cbrt
7×cube-div cos-mult
6×unpow-prod-down pow-unpow cube-prod add-log-exp
4×pow-sqr pow-prod-up
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp flip3-- pow-plus unpow3 frac-add flip-- distribute-lft-out-- difference-of-squares sqr-pow
1×+-commutative pow2 frac-times flip3-+ associate-*r/ swap-sqr associate-*r* associate-*l* associate-*l/ sum-log sum-cubes *-commutative flip-+ distribute-lft-out
Counts
4 → 104
Calls
4 calls:
14.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
9.0ms
(pow (- (- (* (sin x) (sin eps))) (cos x)) 3)
3.0ms
(pow (* (cos x) (cos eps)) 3)
28.0ms
(+ (pow (* (cos x) (cos eps)) 3) (pow (- (- (* (sin x) (sin eps))) (cos x)) 3))

series613.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
91.0ms
(pow (- (- (* (sin x) (sin eps))) (cos x)) 3)
56.0ms
(pow (* (cos x) (cos eps)) 3)
407.0ms
(+ (pow (* (cos x) (cos eps)) 3) (pow (- (- (* (sin x) (sin eps))) (cos x)) 3))

simplify101.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
05521038
12822955
25002950

prune338.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 15.4b

regimes323.0ms

Accuracy

82.1% (1.7b remaining)

Error of 16.7b against oracle of 15.0b and baseline of 24.6b

bsearch114.0ms

Steps
ItersRangePoint
10
9.316647860064626e-18
0.006665254470786589
4.6754847779555244e-08
6
-1.8496456666423901e-16
-1.9909943074331788e-17
-1.8216181721535518e-16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05151
15551
25551

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s4473×body1280valid
571.0ms667×body2560valid
385.0ms1820×body640valid
96.0ms658×body320valid
35.0ms306×body160valid
4.0ms76×body80valid