Details

Time bar (total: 15.7s)

sample166.0ms

Algorithm
intervals
Results
80.0ms108×body1280valid
29.0ms19×body2560valid
23.0ms48×body640valid
17.0ms25×body320valid
4.0ms42×body80valid
3.0ms14×body160valid

simplify14.0ms

Calls
1 calls:
Slowest
14.0ms
(- (sin (+ x eps)) (sin x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize14.0ms

Local error

Found 2 expressions with local error:

3.0b
(sin (+ x eps))
1.6b
(- (sin (+ x eps)) (sin x))

rewrite47.0ms

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
44.0ms
(- (sin (+ x eps)) (sin x))
2.0ms
(sin (+ x eps))

series61.0ms

Calls
2 calls:
Slowest
45.0ms
(- (sin (+ x eps)) (sin x))
16.0ms
(sin (+ x eps))

simplify1.1s

Calls
33 calls:
Slowest
183.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
70.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
63.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
60.0ms
(fma 1 (sin (+ x eps)) (- (* (sin x) 1)))
56.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))

prune495.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite13.0ms

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))

series113.0ms

Calls
3 calls:
Slowest
64.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
32.0ms
(cos (/ (+ x (+ eps x)) 2))
16.0ms
(+ x (+ eps x))

simplify969.0ms

Calls
17 calls:
Slowest
267.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
190.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
158.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
50.0ms
(cos (* 1/2 (+ (* 2 x) eps)))
46.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune606.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(log1p (cos (/ (+ x (+ eps x)) 2)))
0.2b
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (expm1 (log1p (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×expm1-log1p-u
4×insert-posit16 log1p-expm1-u 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
(* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(log1p (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))

series261.0ms

Calls
4 calls:
Slowest
135.0ms
(* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
49.0ms
(log1p (cos (/ (+ x (+ eps x)) 2)))
47.0ms
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
29.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.0s

Calls
22 calls:
Slowest
458.0ms
(- (log 2) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
292.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
239.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
196.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
169.0ms
(* (* (* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))

prune812.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 2 expressions with local error:

3.1b
(cos (fma 1/2 eps x))
0.2b
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))

rewrite14.0ms

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)))
3.0ms
(cos (fma 1/2 eps x))

series63.0ms

Calls
2 calls:
Slowest
48.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
15.0ms
(cos (fma 1/2 eps x))

simplify818.0ms

Calls
15 calls:
Slowest
316.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
187.0ms
(* (* (* (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))))
149.0ms
(- (* 1/2 eps) (+ (* 1/12 (pow eps 3)) (* 1/4 (* x (pow eps 2)))))
45.0ms
(+ (log (cos (fma 1/2 eps x))) (log (sin (/ eps 2))))
37.0ms
(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))

prune439.0ms

Pruning

8 alts after pruning (8 fresh and 0 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

sample7.4s

Algorithm
intervals
Results
3.5s3311×body1280valid
1.7s1826×body640valid
1.0s636×body2560valid
464.0ms347×body160valid
356.0ms814×body320valid
212.0ms1066×body80valid