Details

Time bar (total: 16.3s)

sample220.0ms

Algorithm
intervals
Results
120.0ms105×body1280valid
37.0ms25×body2560valid
34.0ms63×body640valid
10.0ms25×body320valid
4.0ms30×body80valid
4.0ms8×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (sin (+ x eps)) (sin x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize26.0ms

Local error

Found 2 expressions with local error:

3.5b
(sin (+ x eps))
1.1b
(- (sin (+ x eps)) (sin x))

rewrite11.0ms

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
8.0ms
(- (sin (+ x eps)) (sin x))
2.0ms
(sin (+ x eps))

series78.0ms

Calls
2 calls:
Slowest
42.0ms
(- (sin (+ x eps)) (sin x))
36.0ms
(sin (+ x eps))

simplify1.1s

Calls
33 calls:
Slowest
149.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
114.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
79.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
71.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (sin x) 1)))
68.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))

prune314.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

3.7b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Calls
3 calls:
Slowest
8.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
3.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series154.0ms

Calls
3 calls:
Slowest
83.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
38.0ms
(cos (/ (+ x (+ eps x)) 2))
33.0ms
(+ x (+ eps x))

simplify881.0ms

Calls
17 calls:
Slowest
226.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
184.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
127.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
64.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
53.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune936.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

3.7b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.2b
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt 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
Calls
4 calls:
Slowest
12.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
7.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

series348.0ms

Calls
4 calls:
Slowest
150.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
78.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
76.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
44.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.6s

Calls
22 calls:
Slowest
272.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
222.0ms
(- E (+ (* 1/2 (* x (* E eps))) (+ (* 1/2 (* (pow x 2) E)) 1)))
204.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
179.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
166.0ms
(* (* (* (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))))

prune817.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 2 expressions with local error:

3.6b
(cos (fma 1/2 eps x))
0.2b
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×associate-*r* associate-*l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef
Calls
2 calls:
Slowest
9.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
5.0ms
(cos (fma 1/2 eps x))

series87.0ms

Calls
2 calls:
Slowest
55.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
32.0ms
(cos (fma 1/2 eps x))

simplify744.0ms

Calls
15 calls:
Slowest
301.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
154.0ms
(* (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
126.0ms
(- (* 1/2 eps) (+ (* 1/12 (pow eps 3)) (* 1/4 (* x (pow eps 2)))))
37.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
27.0ms
(+ (log (cos (fma 1/2 eps x))) (log (sin (/ eps 2))))

prune400.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes156.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch5.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
4.3s3357×body1280valid
1.8s618×body2560valid
1.4s1809×body640valid
386.0ms801×body320valid
143.0ms1073×body80valid
97.0ms342×body160valid