Details

Time bar (total: 24.1s)

sample206.0ms

Algorithm
intervals
Results
106.0ms100×body1280valid
44.0ms68×body640valid
27.0ms16×body2560valid
12.0ms28×body320valid
5.0ms35×body80valid
3.0ms9×body160valid

simplify8.0ms

Counts
1 → 1
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: 34.9b

localize53.0ms

Local error

Found 2 expressions with local error:

2.6b
(sin (+ x eps))
1.4b
(- (sin (+ x eps)) (sin x))

rewrite86.0ms

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
Counts
2 → 42
Calls
2 calls:
Slowest
67.0ms
(- (sin (+ x eps)) (sin x))
19.0ms
(sin (+ x eps))

series75.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
47.0ms
(- (sin (+ x eps)) (sin x))
28.0ms
(sin (+ x eps))

simplify2.2s

Counts
33 → 48
Calls
33 calls:
Slowest
269.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
229.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
174.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
169.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
165.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune448.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize46.0ms

Local error

Found 4 expressions with local error:

2.5b
(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))))

rewrite72.0ms

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
Counts
4 → 73
Calls
4 calls:
Slowest
32.0ms
(cos (/ (+ x (+ eps x)) 2))
18.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
11.0ms
(+ x (+ eps x))
11.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
101.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
29.0ms
(+ x (+ eps x))
27.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify3.4s

Counts
37 → 85
Calls
37 calls:
Slowest
709.0ms
(* (* (* 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)))))
595.0ms
(* (* (* 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)))))
489.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
362.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
216.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune893.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize73.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
2.5b
(cos (/ (+ x (+ eps x)) 2))
2.5b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Counts
4 → 44
Calls
4 calls:
Slowest
44.0ms
(cos (/ (+ x (+ eps x)) 2))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
34.0ms
(cos (/ (+ x (+ eps x)) 2))
12.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
42.0ms
(cos (/ (+ x (+ eps x)) 2))
33.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
31.0ms
(cos (/ (+ x (+ eps x)) 2))
27.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts
15 → 56
Calls
15 calls:
Slowest
470.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
448.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
435.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
426.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
80.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune749.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize83.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
2.5b
(cos (/ (+ x (+ eps x)) 2))
2.5b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 cos-mult
Counts
4 → 43
Calls
4 calls:
Slowest
37.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(cos (/ (+ x (+ eps x)) 2))
29.0ms
(cos (/ (+ x (+ eps x)) 2))
3.0ms
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

series245.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.7s

Counts
14 → 55
Calls
14 calls:
Slowest
452.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
442.0ms
(- 1 (+ (* 1/3 (* x eps)) (* 1/3 (pow x 2))))
436.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
386.0ms
(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
346.0ms
(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)

prune740.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

regimes233.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch236.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
4.1s3343×body1280valid
1.8s600×body2560valid
1.8s1822×body640valid
333.0ms744×body320valid
244.0ms1153×body80valid
145.0ms338×body160valid