Details

Time bar (total: 24.5s)

sample242.0ms

Algorithm
intervals
Results
123.0ms111×body1280valid
45.0ms23×body2560valid
42.0ms58×body640valid
10.0ms21×body320valid
5.0ms35×body80valid
3.0ms8×body160valid

simplify41.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (sin (+ x eps)) (sin x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize31.0ms

Local error

Found 2 expressions with local error:

3.9b
(sin (+ x eps))
1.5b
(- (sin (+ x eps)) (sin x))

rewrite61.0ms

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
45.0ms
(- (sin (+ x eps)) (sin x))
15.0ms
(sin (+ x eps))

series91.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
50.0ms
(- (sin (+ x eps)) (sin x))
40.0ms
(sin (+ x eps))

simplify2.1s

Counts
33 → 48
Calls
33 calls:
Slowest
252.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
230.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
191.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
163.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
145.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))

prune484.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 3 expressions with local error:

4.0b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite72.0ms

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
41.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
11.0ms
(+ x (+ eps x))

series146.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
83.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
37.0ms
(+ x (+ eps x))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.7s

Counts
25 → 61
Calls
25 calls:
Slowest
489.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
432.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
233.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
78.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
64.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune659.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
0.2b
(* (cos x) (sin eps))
0.2b
(* (sin x) (cos eps))
0.1b
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×add-log-exp
9×prod-diff
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-neg
2×sum-log diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sub-neg fma-def flip3-+ flip3-- associate--l+ flip-+ sin-cos-mult flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 89
Calls
4 calls:
Slowest
81.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
16.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
15.0ms
(* (cos x) (sin eps))
11.0ms
(* (sin x) (cos eps))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
102.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
74.0ms
(* (cos x) (sin eps))
59.0ms
(* (sin x) (cos eps))

simplify5.5s

Counts
61 → 101
Calls
61 calls:
Slowest
497.0ms
(fma (sqrt (+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))) (sqrt (+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
387.0ms
(/ (* (exp (* (sin x) (cos eps))) (exp (* (cos x) (sin eps)))) (exp (sin x)))
349.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos eps) (cos eps)) (cos eps)))
338.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin eps) (sin eps)) (sin eps)))
334.0ms
(fma (* (cbrt (+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))) (cbrt (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))))) (cbrt (+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 3 expressions with local error:

1.6b
(- (* (sin x) (cos eps)) (sin x))
0.2b
(fma (cos x) (sin eps) (- (* (sin x) (cos eps)) (sin x)))
0.2b
(* (sin x) (cos eps))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×pow1 add-cbrt-cube add-exp-log add-log-exp
3×expm1-log1p-u associate-*r* associate-*l* prod-diff insert-posit16 log1p-expm1-u
1×sub-neg flip3-- fma-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef sin-cos-mult flip-- unswap-sqr
Counts
3 → 52
Calls
3 calls:
Slowest
20.0ms
(- (* (sin x) (cos eps)) (sin x))
10.0ms
(* (sin x) (cos eps))
0.0ms
(fma (cos x) (sin eps) (- (* (sin x) (cos eps)) (sin x)))

series312.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
164.0ms
(fma (cos x) (sin eps) (- (* (sin x) (cos eps)) (sin x)))
81.0ms
(- (* (sin x) (cos eps)) (sin x))
67.0ms
(* (sin x) (cos eps))

simplify1.7s

Counts
28 → 61
Calls
28 calls:
Slowest
369.0ms
(fma (sin x) (cos eps) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
295.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos eps) (cos eps)) (cos eps)))
202.0ms
(- x (+ (* 1/2 (* x (pow eps 2))) (* 1/6 (pow x 3))))
193.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
173.0ms
(/ (exp (* (sin x) (cos eps))) (exp (sin x)))

prune625.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes248.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
4.0s3352×body1280valid
1.8s1809×body640valid
1.4s646×body2560valid
624.0ms337×body160valid
345.0ms791×body320valid
147.0ms1065×body80valid