Details

Time bar (total: 22.8s)

sample248.0ms

Algorithm
intervals
Results
150.0ms111×body1280valid
36.0ms23×body2560valid
32.0ms58×body640valid
10.0ms21×body320valid
5.0ms35×body80valid
2.0ms8×body160valid

simplify16.0ms

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: 35.3b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite83.0ms

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
69.0ms
(- (sin (+ x eps)) (sin x))
14.0ms
(sin (+ x eps))

series88.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
54.0ms
(- (sin (+ x eps)) (sin x))
34.0ms
(sin (+ x eps))

simplify836.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
416.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
255.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
47.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
43.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
15.0ms
(- (sin (+ x eps)) (sin x))

prune347.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

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))

rewrite86.0ms

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
37.0ms
(cos (/ (+ x (+ eps x)) 2))
27.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
21.0ms
(+ x (+ eps x))

series134.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
70.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
32.0ms
(+ x (+ eps x))
31.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.3s

Counts
23 → 52
Calls
23 calls:
Slowest
384.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
221.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
162.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
67.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
46.0ms
(* (sqrt (cos (/ (+ x (+ eps x)) 2))) (sqrt (sin (/ eps 2))))

prune535.0ms

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)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×insert-posit16
2×sum-log diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sub-neg flip3-+ flip3-- associate--l+ flip-+ sin-cos-mult flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
Slowest
69.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
16.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
10.0ms
(* (cos x) (sin eps))
10.0ms
(* (sin x) (cos eps))

series434.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
146.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
71.0ms
(* (sin x) (cos eps))
70.0ms
(* (cos x) (sin eps))

simplify2.9s

Counts
40 → 80
Calls
40 calls:
Slowest
400.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
374.0ms
(/ (* (exp (* (sin x) (cos eps))) (exp (* (cos x) (sin eps)))) (exp (sin x)))
363.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin eps) (sin eps)) (sin eps)))
342.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos eps) (cos eps)) (cos eps)))
233.0ms
(* (exp (* (sin x) (cos eps))) (exp (* (cos x) (sin eps))))

prune939.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize56.0ms

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
(- (* (cos x) (sin eps)) (sin x))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-log-exp
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×insert-posit16
3×sin-cos-mult
2×associate-+r+ sum-log sub-neg flip3-- diff-log pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-- unswap-sqr
1×+-commutative associate-+r- flip3-+ flip-+
Counts
4 → 70
Calls
4 calls:
Slowest
31.0ms
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
23.0ms
(- (* (cos x) (sin eps)) (sin x))
20.0ms
(* (sin x) (cos eps))
16.0ms
(* (cos x) (sin eps))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
104.0ms
(- (* (cos x) (sin eps)) (sin x))
78.0ms
(* (cos x) (sin eps))
65.0ms
(* (sin x) (cos eps))

simplify4.1s

Counts
43 → 82
Calls
43 calls:
Slowest
477.0ms
(- (+ (* 1/6 (pow x 3)) eps) x)
421.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
390.0ms
(+ (* (+ (sin (- x eps)) (sin (+ x eps))) (+ (* (cos x) (sin eps)) (sin x))) (* 2 (- (* (* (cos x) (sin eps)) (* (cos x) (sin eps))) (* (sin x) (sin x)))))
372.0ms
(* (exp (* (sin x) (cos eps))) (exp (- (* (cos x) (sin eps)) (sin x))))
365.0ms
(* 2 (+ (* (* (cos x) (sin eps)) (* (cos x) (sin eps))) (+ (* (sin x) (sin x)) (* (* (cos x) (sin eps)) (sin x)))))

prune827.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes282.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 15.2b

bsearch197.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.0s3352×body1280valid
1.5s646×body2560valid
1.3s1809×body640valid
379.0ms791×body320valid
190.0ms1065×body80valid
92.0ms337×body160valid