Details

Time bar (total: 28.7s)

sample159.0ms

Algorithm
intervals
Results
85.0ms97×body1280valid
26.0ms59×body640valid
25.0ms21×body2560valid
8.0ms24×body320valid
4.0ms42×body80valid
3.0ms13×body160valid

simplify9.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize26.0ms

Local error

Found 2 expressions with local error:

2.7b
(sin (+ x eps))
1.6b
(- (sin (+ x eps)) (sin x))

rewrite80.0ms

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
65.0ms
(- (sin (+ x eps)) (sin x))
15.0ms
(sin (+ x eps))

series87.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
56.0ms
(- (sin (+ x eps)) (sin x))
31.0ms
(sin (+ x eps))

simplify3.4s

Counts
61 → 48
Calls
61 calls:
Slowest
409.0ms
(* (* (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x))) (- (sin (+ x eps)) (sin x)))
256.0ms
(- (pow (sin (+ x eps)) 3) (pow (sin x) 3))
241.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
209.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
199.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))

prune421.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize39.0ms

Local error

Found 3 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
6×add-cube-cbrt
5×pow1 add-cbrt-cube add-exp-log
3×expm1-log1p-u sum-log fma-def associate-*r* associate-*l* insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
3 → 52
Calls
3 calls:
Slowest
39.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
22.0ms
(+ x (+ eps x))

series157.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
82.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
34.0ms
(+ x (+ eps x))

simplify3.7s

Counts
59 → 61
Calls
59 calls:
Slowest
431.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
419.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
322.0ms
(+ (* x x) (- (* (+ eps x) (+ eps x)) (* x (+ eps x))))
267.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
247.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune712.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.2b
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.2b
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 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 unswap-sqr
Counts
4 → 55
Calls
4 calls:
Slowest
23.0ms
(cos (/ (+ x (+ eps x)) 2))
14.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
97.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
64.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
27.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify4.2s

Counts
65 → 67
Calls
65 calls:
Slowest
451.0ms
(* (* (* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
432.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
400.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
231.0ms
(- E (+ (* 1/2 (* x (* E eps))) (+ (* 1/2 (* (pow x 2) E)) 1)))
217.0ms
(* (* (* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2))) (* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))) (* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2))))

prune947.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
2.7b
(cos (/ (+ x (+ eps x)) 2))
2.7b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite152.0ms

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
48.0ms
(cos (/ (+ x (+ eps x)) 2))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
38.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series142.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
40.0ms
(cos (/ (+ x (+ eps x)) 2))
39.0ms
(cos (/ (+ x (+ eps x)) 2))
37.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
27.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify4.0s

Counts
56 → 56
Calls
56 calls:
Slowest
455.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
425.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
423.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
397.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
120.0ms
(log (cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2)))))

prune791.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

regimes197.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.3b

bsearch257.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.3s3329×body1280valid
1.8s1859×body640valid
1.7s622×body2560valid
350.0ms785×body320valid
155.0ms1073×body80valid
96.0ms332×body160valid