Details

Time bar (total: 18.9s)

sample207.0ms

Algorithm
intervals
Results
105.0ms106×body1280valid
36.0ms61×body640valid
33.0ms17×body2560valid
12.0ms28×body320valid
4.0ms35×body80valid
3.0ms9×body160valid

simplify16.0ms

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

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize15.0ms

Local error

Found 2 expressions with local error:

4.4b
(sin (+ x eps))
1.0b
(- (sin (+ x eps)) (sin x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube sin-sum add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 26
Calls
2 calls:
Slowest
55.0ms
(- (sin (+ x eps)) (sin x))
7.0ms
(sin (+ x eps))

series88.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
55.0ms
(- (sin (+ x eps)) (sin x))
33.0ms
(sin (+ x eps))

simplify829.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
426.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
221.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
54.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
21.0ms
(- (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune280.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 3 expressions with local error:

4.3b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
5×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r* associate-*l* insert-posit16 distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
38.0ms
(cos (/ (+ x (+ eps x)) 2))
22.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
21.0ms
(+ x (+ eps x))

series159.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
90.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
44.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(+ x (+ eps x))

simplify1.5s

Counts
23 → 52
Calls
23 calls:
Slowest
391.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
309.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
220.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
69.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
67.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune597.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

4.3b
(cos (/ (+ x (+ eps x)) 2))
4.3b
(cos (/ (+ x (+ eps x)) 2))
4.3b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Counts
4 → 36
Calls
4 calls:
Slowest
36.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cos (/ (+ x (+ eps x)) 2))
21.0ms
(cos (/ (+ x (+ eps x)) 2))
18.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
46.0ms
(cos (/ (+ x (+ eps x)) 2))
43.0ms
(cos (/ (+ x (+ eps x)) 2))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
39.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

simplify1.6s

Counts
15 → 48
Calls
15 calls:
Slowest
286.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
276.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
274.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
267.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
78.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune714.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

4.3b
(cos (/ (+ x (+ eps x)) 2))
4.3b
(cos (/ (+ x (+ eps x)) 2))
4.3b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×cbrt-prod cbrt-div pow1/3 cos-mult
Counts
4 → 35
Calls
4 calls:
Slowest
26.0ms
(cos (/ (+ x (+ eps x)) 2))
22.0ms
(cos (/ (+ x (+ eps x)) 2))
18.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))
47.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.1s

Counts
14 → 47
Calls
14 calls:
Slowest
391.0ms
(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
368.0ms
(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
305.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
276.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
243.0ms
(- 1 (+ (* 1/3 (* x eps)) (* 1/3 (pow x 2))))

prune660.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

regimes155.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.5b

bsearch202.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.1s3285×body1280valid
1.5s1870×body640valid
1.4s618×body2560valid
353.0ms793×body320valid
200.0ms1103×body80valid
100.0ms331×body160valid