Details

Time bar (total: 24.1s)

sample248.0ms

Algorithm
intervals
Results
150.0ms144×body1280valid
37.0ms18×body2560valid
35.0ms60×body640valid
10.0ms24×body320valid
2.0ms8×body160valid
0.0ms2×body80valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (cos (+ x eps)) (cos x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize14.0ms

Local error

Found 2 expressions with local error:

5.6b
(cos (+ x eps))
0.5b
(- (cos (+ x eps)) (cos x))

rewrite412.0ms

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
402.0ms
(- (cos (+ x eps)) (cos x))
9.0ms
(cos (+ x eps))

series120.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
90.0ms
(- (cos (+ x eps)) (cos x))
29.0ms
(cos (+ x eps))

simplify1.9s

Counts
33 → 48
Calls
33 calls:
Slowest
222.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
207.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
192.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
169.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
166.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune507.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

5.5b
(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))))

rewrite177.0ms

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
68.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
63.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
24.0ms
(sin (/ (+ x (+ eps x)) 2))
21.0ms
(+ x (+ eps x))

series315.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
103.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
49.0ms
(sin (/ (+ x (+ eps x)) 2))
34.0ms
(+ x (+ eps x))

simplify3.6s

Counts
38 → 87
Calls
38 calls:
Slowest
653.0ms
(* (* (* -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)))))
569.0ms
(* (* (* -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)))))
485.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
330.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
292.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 3 expressions with local error:

5.5b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite112.0ms

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
62.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
29.0ms
(sin (/ (+ x (+ eps x)) 2))
20.0ms
(+ x (+ eps x))

series190.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
37.0ms
(sin (/ (+ x (+ eps x)) 2))
36.0ms
(+ x (+ eps x))

simplify2.1s

Counts
24 → 61
Calls
24 calls:
Slowest
552.0ms
(* (* (* (* -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))))
541.0ms
(* (* (* (* -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))))
248.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
210.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
69.0ms
(+ (+ (log -2) (log (sin (/ (+ x (+ eps x)) 2)))) (log (sin (/ eps 2))))

prune791.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

5.5b
(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)))
0.3b
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

rewrite68.0ms

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
43.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
0.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
101.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
87.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
52.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.6s

Counts
23 → 67
Calls
23 calls:
Slowest
530.0ms
(* (* (* (* -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))))
525.0ms
(* (* (* (* -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))))
261.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
236.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
212.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune788.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

regimes255.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.0b

bsearch321.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.1s4519×body1280valid
2.1s1798×body640valid
1.1s644×body2560valid
410.0ms649×body320valid
76.0ms302×body160valid
11.0ms88×body80valid