Details

Time bar (total: 24.5s)

sample229.0ms

Algorithm
intervals
Results
120.0ms107×body1280valid
42.0ms60×body640valid
36.0ms19×body2560valid
8.0ms18×body320valid
7.0ms43×body80valid
3.0ms9×body160valid

simplify10.0ms

Calls
1 calls:
Slowest
10.0ms
(- (sin (+ x eps)) (sin x))

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize15.0ms

Local error

Found 2 expressions with local error:

3.4b
(sin (+ x eps))
1.1b
(- (sin (+ x eps)) (sin x))

rewrite48.0ms

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 add-cbrt-cube sin-sum add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
40.0ms
(- (sin (+ x eps)) (sin x))
7.0ms
(sin (+ x eps))

series83.0ms

Calls
2 calls:
Slowest
45.0ms
(- (sin (+ x eps)) (sin x))
38.0ms
(sin (+ x eps))

simplify2.2s

Calls
33 calls:
Slowest
266.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
198.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
193.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
184.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
179.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune430.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite90.0ms

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
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Calls
4 calls:
Slowest
39.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
21.0ms
(+ x (+ eps x))
19.0ms
(cos (/ (+ x (+ eps x)) 2))
10.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series264.0ms

Calls
4 calls:
Slowest
108.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
90.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
33.0ms
(cos (/ (+ x (+ eps x)) 2))
32.0ms
(+ x (+ eps x))

simplify3.5s

Calls
37 calls:
Slowest
981.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
535.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
408.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
332.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
242.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))

prune839.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.3b
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))

rewrite67.0ms

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
39.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
1.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

series328.0ms

Calls
4 calls:
Slowest
131.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
89.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
64.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
44.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.4s

Calls
24 calls:
Slowest
405.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
372.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
366.0ms
(* (* (* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
307.0ms
(- E (+ (* 1/2 (* x (* E eps))) (+ (* 1/2 (* (pow x 2) E)) 1)))
242.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune982.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Calls
4 calls:
Slowest
74.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
73.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
45.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))

series232.0ms

Calls
4 calls:
Slowest
92.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
67.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
45.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify2.7s

Calls
36 calls:
Slowest
428.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
422.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
390.0ms
(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
226.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
213.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune930.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes199.0ms

Accuracy

97.9% (0.3b remaining)

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

bsearch235.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.9s3277×body1280valid
2.2s1880×body640valid
1.4s660×body2560valid
357.0ms722×body320valid
149.0ms1097×body80valid
104.0ms364×body160valid