Details

Time bar (total: 24.2s)

sample189.0ms

Algorithm
intervals
Results
105.0ms127×body1280valid
33.0ms74×body640valid
28.0ms18×body2560valid
7.0ms23×body320valid
3.0ms12×body160valid
0.0ms2×body80valid

simplify16.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize19.0ms

Local error

Found 2 expressions with local error:

3.9b
(cos (+ x eps))
1.8b
(- (cos (+ x eps)) (cos x))

rewrite64.0ms

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
37.0ms
(cos (+ x eps))
26.0ms
(- (cos (+ x eps)) (cos x))

series104.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(- (cos (+ x eps)) (cos x))
28.0ms
(cos (+ x eps))

simplify2.0s

Counts
33 → 48
Calls
33 calls:
Slowest
247.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
194.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
181.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
180.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
158.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune471.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

3.8b
(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))))

rewrite167.0ms

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
74.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
60.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
20.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
94.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
43.0ms
(sin (/ (+ x (+ eps x)) 2))
38.0ms
(+ x (+ eps x))

simplify3.1s

Counts
38 → 87
Calls
38 calls:
Slowest
587.0ms
(* (* (* -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)))))
535.0ms
(* (* (* -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)))))
368.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
315.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
228.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

3.8b
(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
64.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
24.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(+ x (+ eps x))

series170.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
112.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
31.0ms
(sin (/ (+ x (+ eps x)) 2))
28.0ms
(+ x (+ eps x))

simplify2.2s

Counts
24 → 61
Calls
24 calls:
Slowest
570.0ms
(* (* (* (* -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))))
540.0ms
(* (* (* (* -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))))
252.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
246.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
60.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune687.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 4 expressions with local error:

3.8b
(sin (/ (+ x (+ eps x)) 2))
0.5b
(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))))

rewrite76.0ms

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))
35.0ms
(* (* -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))))

series373.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
71.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
61.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
44.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.8s

Counts
23 → 67
Calls
23 calls:
Slowest
559.0ms
(* (* (* (* -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))))
543.0ms
(* (* (* (* -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))))
357.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
251.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
197.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))

prune882.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes351.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch255.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.2s4465×body1280valid
1.5s606×body2560valid
1.3s1830×body640valid
351.0ms726×body320valid
122.0ms294×body160valid
10.0ms79×body80valid