Details

Time bar (total: 24.6s)

sample165.0ms

Algorithm
intervals
Results
99.0ms146×body1280valid
27.0ms65×body640valid
21.0ms17×body2560valid
6.0ms19×body320valid
1.0ms6×body160valid
0.0ms3×body80valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize56.0ms

Local error

Found 2 expressions with local error:

4.4b
(cos (+ x eps))
0.5b
(- (cos (+ x eps)) (cos x))

rewrite29.0ms

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
14.0ms
(- (cos (+ x eps)) (cos x))
14.0ms
(cos (+ x eps))

series113.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
96.0ms
(- (cos (+ x eps)) (cos x))
17.0ms
(cos (+ x eps))

simplify2.2s

Counts
33 → 48
Calls
33 calls:
Slowest
269.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
211.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
203.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
173.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
170.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune440.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

4.2b
(sin (/ (+ x (+ eps x)) 2))
0.2b
(* (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
84.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
62.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
19.0ms
(sin (/ (+ x (+ eps x)) 2))
11.0ms
(+ x (+ eps x))

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
104.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms
(+ x (+ eps x))
34.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify3.4s

Counts
38 → 87
Calls
38 calls:
Slowest
670.0ms
(* (* (* -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)))))
571.0ms
(* (* (* -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)))))
481.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
280.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
261.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 3 expressions with local error:

4.2b
(sin (/ (+ x (+ eps x)) 2))
0.2b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite143.0ms

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
80.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
39.0ms
(sin (/ (+ x (+ eps x)) 2))
22.0ms
(+ x (+ eps x))

series228.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
133.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
52.0ms
(sin (/ (+ x (+ eps x)) 2))
42.0ms
(+ x (+ eps x))

simplify2.6s

Counts
24 → 61
Calls
24 calls:
Slowest
900.0ms
(* (* (* (* -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))))
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))))
364.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
263.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
64.0ms
(sin (* 1/2 (+ (* 2 x) eps)))

prune739.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

4.2b
(sin (/ (+ x (+ eps x)) 2))
0.4b
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.2b
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.2b
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

rewrite44.0ms

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
24.0ms
(sin (/ (+ x (+ eps x)) 2))
18.0ms
(* (* -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)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
96.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
90.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
33.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.9s

Counts
23 → 67
Calls
23 calls:
Slowest
612.0ms
(* (* (* (* -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))))
589.0ms
(* (* (* (* -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))))
270.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
252.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
250.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune772.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

regimes339.0ms

Accuracy

94.9% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 16.1b

bsearch302.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
4.3s4453×body1280valid
2.1s1900×body640valid
1.2s618×body2560valid
267.0ms689×body320valid
64.0ms253×body160valid
11.0ms87×body80valid