Details

Time bar (total: 28.2s)

sample228.0ms

Algorithm
intervals
Results
97.0ms107×body1280valid
69.0ms60×body640valid
28.0ms18×body2560valid
13.0ms29×body320valid
4.0ms15×body160valid
4.0ms27×body80valid

simplify17.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize23.0ms

Local error

Found 2 expressions with local error:

3.1b
(sin (+ x eps))
1.6b
(- (sin (+ x eps)) (sin x))

rewrite69.0ms

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
60.0ms
(- (sin (+ x eps)) (sin x))
8.0ms
(sin (+ x eps))

series74.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
52.0ms
(- (sin (+ x eps)) (sin x))
22.0ms
(sin (+ x eps))

simplify3.1s

Counts
61 → 48
Calls
61 calls:
Slowest
381.0ms
(* (* (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x))) (- (sin (+ x eps)) (sin x)))
249.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
218.0ms
(- (pow (sin (+ x eps)) 3) (pow (sin x) 3))
179.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
173.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune484.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 3 expressions with local error:

3.0b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite65.0ms

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
25.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(+ x (+ eps x))
15.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series198.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
109.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
45.0ms
(+ x (+ eps x))
44.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify3.9s

Counts
59 → 61
Calls
59 calls:
Slowest
448.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
387.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
353.0ms
(+ (* x x) (- (* (+ eps x) (+ eps x)) (* x (+ eps x))))
341.0ms
(exp (+ x (+ eps x)))
302.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

prune655.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ x (+ eps x)) 2))
3.0b
(cos (/ (+ x (+ eps x)) 2))
3.0b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite93.0ms

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
27.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(cos (/ (+ x (+ eps x)) 2))
14.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series134.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
34.0ms
(cos (/ (+ x (+ eps x)) 2))
31.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify4.3s

Counts
56 → 56
Calls
56 calls:
Slowest
509.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
490.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
466.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
422.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
114.0ms
(log1p (cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2)))))

prune717.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ x (+ eps x)) 2))
3.0b
(cos (/ (+ x (+ eps x)) 2))
3.0b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (cos (/ (+ x (+ eps x)) 2)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 44
Calls
4 calls:
Slowest
37.0ms
(cos (/ (+ x (+ eps x)) 2))
36.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(cbrt (cos (/ (+ x (+ eps x)) 2)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(cbrt (cos (/ (+ x (+ eps x)) 2)))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
36.0ms
(cos (/ (+ x (+ eps x)) 2))
32.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify4.0s

Counts
58 → 56
Calls
58 calls:
Slowest
464.0ms
(- 1 (+ (* 1/6 (* x eps)) (* 1/6 (pow x 2))))
451.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
439.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
405.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
294.0ms
(pow (cos (* 1/2 (+ (* 2 x) eps))) 1/3)

prune741.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes195.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.6b

bsearch216.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.1s3186×body1280valid
1.9s1804×body640valid
1.6s689×body2560valid
428.0ms821×body320valid
162.0ms1145×body80valid
110.0ms355×body160valid