Details

Time bar (total: 34.6s)

sample233.0ms

Algorithm
intervals
Results
120.0ms140×body1280valid
51.0ms61×body640valid
38.0ms21×body2560valid
10.0ms22×body320valid
3.0ms10×body160valid
0.0ms2×body80valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize27.0ms

Local error

Found 2 expressions with local error:

2.6b
(cos (+ x eps))
1.2b
(- (cos (+ x eps)) (cos x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 cos-sum add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 42
Calls
2 calls:
Slowest
33.0ms
(- (cos (+ x eps)) (cos x))
9.0ms
(cos (+ x eps))

series101.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
72.0ms
(- (cos (+ x eps)) (cos x))
29.0ms
(cos (+ x eps))

simplify3.4s

Counts
61 → 48
Calls
61 calls:
Slowest
404.0ms
(* (* (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)))
228.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
219.0ms
(- (pow (cos (+ x eps)) 3) (pow (cos x) 3))
208.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
206.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))

prune469.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize41.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sum-log fma-def distribute-lft-out
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 75
Calls
4 calls:
Slowest
90.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
88.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
23.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(+ x (+ eps x))

series324.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
118.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
46.0ms
(sin (/ (+ x (+ eps x)) 2))
33.0ms
(+ x (+ eps x))

simplify7.2s

Counts
84 → 87
Calls
84 calls:
Slowest
694.0ms
(* (* (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))) (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
655.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
624.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
393.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
350.0ms
(+ (* x x) (- (* (+ eps x) (+ eps x)) (* x (+ eps x))))

prune992.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 3 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-log-exp
5×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u sum-log fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative associate-+r+ flip3-+ associate-*l* *-commutative flip-+
Counts
3 → 52
Calls
3 calls:
Slowest
68.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
32.0ms
(sin (/ (+ x (+ eps x)) 2))
15.0ms
(+ x (+ eps x))

series222.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
141.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
56.0ms
(sin (/ (+ x (+ eps x)) 2))
26.0ms
(+ x (+ eps x))

simplify5.0s

Counts
58 → 61
Calls
58 calls:
Slowest
725.0ms
(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))) (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))) (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))))
585.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
546.0ms
(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
306.0ms
(+ (* x x) (- (* (+ eps x) (+ eps x)) (* x (+ eps x))))
299.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune709.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize46.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.4b
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.3b
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.2b
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
1×log1p-udef expm1-log1p associate-*l* log1p-expm1 *-commutative expm1-udef
Counts
4 → 55
Calls
4 calls:
Slowest
39.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
1.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
91.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
66.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
33.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify5.6s

Counts
64 → 67
Calls
64 calls:
Slowest
903.0ms
(* (* (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
722.0ms
(* (* (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2))) (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))) (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2))))
605.0ms
(* (* (* (* -2 -2) -2) (* (* (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
310.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
273.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune707.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.5b

regimes201.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.4b

bsearch226.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.1s4514×body1280valid
1.2s1867×body640valid
1.2s622×body2560valid
382.0ms659×body320valid
65.0ms257×body160valid
10.0ms81×body80valid