Details

Time bar (total: 19.6s)

sample254.0ms

Algorithm
intervals
Results
112.0ms109×body1280valid
66.0ms55×body640valid
48.0ms25×body2560valid
9.0ms20×body320valid
6.0ms39×body80valid
2.0ms8×body160valid

simplify8.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize12.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (sin (+ x eps)) (sin x))
1.6b
(sin (+ x eps))

rewrite16.0ms

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
14.0ms
(- (sin (+ x eps)) (sin x))
2.0ms
(sin (+ x eps))

series78.0ms

Calls
2 calls:
Slowest
55.0ms
(- (sin (+ x eps)) (sin x))
23.0ms
(sin (+ x eps))

simplify1.2s

Calls
33 calls:
Slowest
163.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
76.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
70.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (sqrt (sin x)) (sqrt (sin x)))))
63.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
57.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (sqrt (sin x)) (sqrt (sin x)))))

prune349.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 3 expressions with local error:

1.6b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite23.0ms

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
15.0ms
(* (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
84.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
26.0ms
(cos (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

simplify863.0ms

Calls
17 calls:
Slowest
200.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
153.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
148.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
75.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
59.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune618.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 2 expressions with local error:

1.6b
(cos (fma 1/2 eps x))
0.2b
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))

rewrite16.0ms

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
11.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
4.0ms
(cos (fma 1/2 eps x))

series62.0ms

Calls
2 calls:
Slowest
47.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
14.0ms
(cos (fma 1/2 eps x))

simplify796.0ms

Calls
15 calls:
Slowest
366.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
166.0ms
(- (* 1/2 eps) (+ (* 1/12 (pow eps 3)) (* 1/4 (* x (pow eps 2)))))
96.0ms
(* (* (* (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))))
33.0ms
(+ (log (cos (fma 1/2 eps x))) (log (sin (/ eps 2))))
30.0ms
(* (cbrt (cos (fma 1/2 eps x))) (cbrt (cos (fma 1/2 eps x))))

prune436.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
0.1b
(* (sin (* 1/2 eps)) (sin x))
0.1b
(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
0.1b
(* (cos (* 1/2 eps)) (cos x))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
5×cos-mult sin-mult
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod
2×flip3-- frac-sub flip-- sub-div
1×sub-neg fma-neg diff-log prod-diff
Calls
4 calls:
Slowest
35.0ms
(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
25.0ms
(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
16.0ms
(* (cos (* 1/2 eps)) (cos x))
14.0ms
(* (sin (* 1/2 eps)) (sin x))

series360.0ms

Calls
4 calls:
Slowest
142.0ms
(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
118.0ms
(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
58.0ms
(* (sin (* 1/2 eps)) (sin x))
43.0ms
(* (cos (* 1/2 eps)) (cos x))

simplify4.6s

Calls
49 calls:
Slowest
615.0ms
(* (- (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))) (sin (/ eps 2)))
542.0ms
(* (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
404.0ms
(* (- (pow (* (cos (* 1/2 eps)) (cos x)) 3) (pow (* (sin (* 1/2 eps)) (sin x)) 3)) (sin (/ eps 2)))
397.0ms
(- (* (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) 2) (* 2 (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))))
366.0ms
(- (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.9s3268×body1280valid
1.5s715×body2560valid
1.3s1824×body640valid
1.1s758×body320valid
140.0ms1090×body80valid
95.0ms345×body160valid