Details

Time bar (total: 17.9s)

sample238.0ms

Algorithm
intervals
Results
98.0ms99×body1280valid
51.0ms28×body2560valid
37.0ms59×body640valid
34.0ms24×body320valid
5.0ms34×body80valid
3.0ms12×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (sin (+ x eps)) (sin x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize12.0ms

Local error

Found 2 expressions with local error:

2.5b
(sin (+ x eps))
1.5b
(- (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))

series76.0ms

Calls
2 calls:
Slowest
54.0ms
(- (sin (+ x eps)) (sin x))
21.0ms
(sin (+ x eps))

simplify1.2s

Calls
33 calls:
Slowest
193.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
96.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
69.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
61.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
60.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (sin x) 1)))

prune452.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* 2 (* (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
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×*-commutative
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+
Calls
4 calls:
Slowest
9.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
7.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
3.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series145.0ms

Calls
4 calls:
Slowest
61.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
54.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
17.0ms
(cos (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

simplify1.4s

Calls
21 calls:
Slowest
301.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
210.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
203.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
163.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
73.0ms
(* 2 (* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune797.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1 add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative associate-+r+ flip3-+ associate-*l* pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Calls
3 calls:
Slowest
18.0ms
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series122.0ms

Calls
3 calls:
Slowest
78.0ms
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
29.0ms
(cos (/ (+ x (+ eps x)) 2))
15.0ms
(+ x (+ eps x))

simplify1.3s

Calls
15 calls:
Slowest
429.0ms
(* (* (* (* 2 (cos (/ (+ x (+ eps x)) 2))) (* 2 (cos (/ (+ x (+ eps x)) 2)))) (* 2 (cos (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
247.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
195.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
81.0ms
(* 2 (* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
69.0ms
(* 2 (* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.3b
(* (* 2 (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.2b
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r*
1×log1p-udef expm1-log1p associate-*l* pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef
Calls
4 calls:
Slowest
16.0ms
(* (* 2 (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

series281.0ms

Calls
4 calls:
Slowest
147.0ms
(* (* 2 (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
54.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
52.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
28.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.9s

Calls
20 calls:
Slowest
372.0ms
(* (* (* (* 2 (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (* 2 (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))) (* 2 (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
283.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
268.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
228.0ms
(- E (+ (* 1/2 (* x (* E eps))) (+ (* 1/2 (* (pow x 2) E)) 1)))
174.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))

prune713.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

regimes171.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.9b

bsearch261.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.7s3234×body1280valid
1.8s658×body2560valid
1.7s1829×body640valid
356.0ms804×body320valid
291.0ms1119×body80valid
147.0ms356×body160valid