Details

Time bar (total: 25.1s)

sample214.0ms

Algorithm
intervals
Results
123.0ms150×body1280valid
41.0ms59×body640valid
31.0ms19×body2560valid
8.0ms17×body320valid
2.0ms8×body160valid
0.0ms3×body80valid

simplify8.0ms

Calls
1 calls:
Slowest
8.0ms
(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize46.0ms

Local error

Found 2 expressions with local error:

3.5b
(cos (+ x eps))
0.9b
(- (cos (+ x eps)) (cos x))

rewrite39.0ms

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
Calls
2 calls:
Slowest
23.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

series102.0ms

Calls
2 calls:
Slowest
74.0ms
(- (cos (+ x eps)) (cos x))
28.0ms
(cos (+ x eps))

simplify2.4s

Calls
33 calls:
Slowest
252.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
238.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
198.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
179.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (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))))))

prune453.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

3.3b
(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))))

rewrite204.0ms

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
Calls
4 calls:
Slowest
88.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
68.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
24.0ms
(sin (/ (+ x (+ eps x)) 2))
22.0ms
(+ x (+ eps x))

series297.0ms

Calls
4 calls:
Slowest
131.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
101.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
35.0ms
(sin (/ (+ x (+ eps x)) 2))
30.0ms
(+ x (+ eps x))

simplify3.3s

Calls
38 calls:
Slowest
685.0ms
(* (* (* -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)))))
564.0ms
(* (* (* -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)))))
415.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
277.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
243.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))

prune924.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

3.3b
(sin (/ (+ x (+ eps x)) 2))
0.2b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b
(log1p (expm1 (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))))
0.1b
(expm1 (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 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
Calls
4 calls:
Slowest
45.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
45.0ms
(sin (/ (+ x (+ eps x)) 2))
0.0ms
(expm1 (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
0.0ms
(log1p (expm1 (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))))

series560.0ms

Calls
4 calls:
Slowest
206.0ms
(expm1 (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
205.0ms
(log1p (expm1 (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))))
112.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
37.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify3.0s

Calls
24 calls:
Slowest
504.0ms
(- (exp (* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))) 1)
437.0ms
(- (exp (* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))) 1)
359.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
329.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
279.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune852.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.2b
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.2b
(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef unswap-sqr
Calls
4 calls:
Slowest
45.0ms
(sin (/ (+ x (+ eps x)) 2))
9.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series359.0ms

Calls
4 calls:
Slowest
146.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
89.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
81.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
42.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.0s

Calls
24 calls:
Slowest
430.0ms
(* (* (* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
304.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
298.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
279.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
84.0ms
(+ x (+ (* 1/2 (pow x 2)) (* 1/2 eps)))

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes250.0ms

Accuracy

98.1% (0.3b remaining)

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

bsearch237.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
5.1s4391×body1280valid
1.3s1891×body640valid
1.2s660×body2560valid
412.0ms84×body80valid
330.0ms679×body320valid
74.0ms295×body160valid