Details

Time bar (total: 24.6s)

sample216.0ms

Algorithm
intervals
Results
104.0ms140×body1280valid
53.0ms54×body640valid
34.0ms23×body2560valid
9.0ms27×body320valid
2.0ms6×body160valid
1.0ms6×body80valid

simplify16.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize15.0ms

Local error

Found 2 expressions with local error:

2.7b
(cos (+ x eps))
1.4b
(- (cos (+ x eps)) (cos x))

rewrite383.0ms

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
375.0ms
(- (cos (+ x eps)) (cos x))
7.0ms
(cos (+ x eps))

series107.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
80.0ms
(- (cos (+ x eps)) (cos x))
27.0ms
(cos (+ x eps))

simplify2.2s

Counts
33 → 48
Calls
33 calls:
Slowest
267.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
198.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
196.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
165.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
164.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune457.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

2.7b
(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))))

rewrite176.0ms

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
58.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
54.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
44.0ms
(sin (/ (+ x (+ eps x)) 2))
19.0ms
(+ x (+ eps x))

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
138.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms
(+ x (+ eps x))
37.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify3.4s

Counts
38 → 87
Calls
38 calls:
Slowest
698.0ms
(* (* (* -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)))))
558.0ms
(* (* (* -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)))))
372.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
284.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
282.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune872.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 3 expressions with local error:

2.7b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite134.0ms

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
85.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
26.0ms
(sin (/ (+ x (+ eps x)) 2))
22.0ms
(+ x (+ eps x))

series255.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
159.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
55.0ms
(sin (/ (+ x (+ eps x)) 2))
41.0ms
(+ x (+ eps x))

simplify2.3s

Counts
24 → 61
Calls
24 calls:
Slowest
581.0ms
(* (* (* (* -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))))
537.0ms
(* (* (* (* -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))))
311.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
232.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
96.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune745.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize62.0ms

Local error

Found 4 expressions with local error:

2.7b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b
(expm1 (log1p (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
0.1b
(log1p (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod sin-mult expm1-udef unswap-sqr
Counts
4 → 56
Calls
4 calls:
Slowest
60.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
46.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(log1p (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
0.0ms
(expm1 (log1p (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(expm1 (log1p (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
197.0ms
(log1p (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
118.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
37.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.5s

Counts
25 → 68
Calls
25 calls:
Slowest
413.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
348.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
339.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
325.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
296.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune868.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

regimes176.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.2b

bsearch297.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.9s4452×body1280valid
1.6s1834×body640valid
1.2s658×body2560valid
305.0ms692×body320valid
112.0ms292×body160valid
10.0ms72×body80valid