Details

Time bar (total: 22.6s)

sample204.0ms

Algorithm
intervals
Results
105.0ms147×body1280valid
44.0ms16×body2560valid
30.0ms54×body640valid
10.0ms30×body320valid
2.0ms7×body160valid
0.0ms2×body80valid

simplify14.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize13.0ms

Local error

Found 2 expressions with local error:

2.7b
(cos (+ x eps))
1.2b
(- (cos (+ x eps)) (cos x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 cos-sum add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 26
Calls
2 calls:
Slowest
35.0ms
(- (cos (+ x eps)) (cos x))
7.0ms
(cos (+ x eps))

series105.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(- (cos (+ x eps)) (cos x))
29.0ms
(cos (+ x eps))

simplify1.1s

Counts
32 → 32

prune363.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 3 expressions with local error:

2.6b
(sin (/ (+ x (+ x eps)) 2))
0.3b
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
0.0b
(+ x (+ x eps))

rewrite127.0ms

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-+ sin-mult unswap-sqr
Counts
3 → 44
Calls
3 calls:
Slowest
59.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
44.0ms
(sin (/ (+ x (+ x eps)) 2))
23.0ms
(+ x (+ x eps))

series190.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
105.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
58.0ms
(sin (/ (+ x (+ x eps)) 2))
26.0ms
(+ x (+ x eps))

simplify3.3s

Counts
53 → 53

prune640.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ x eps)) 2))
0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
Counts
4 → 44
Calls
4 calls:
Slowest
25.0ms
(sin (/ (+ x (+ x eps)) 2))
3.0ms
(cbrt (sin (/ eps 2)))
3.0ms
(cbrt (sin (/ eps 2)))
3.0ms
(cbrt (sin (/ eps 2)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(cbrt (sin (/ eps 2)))
163.0ms
(cbrt (sin (/ eps 2)))
142.0ms
(cbrt (sin (/ eps 2)))
55.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify3.2s

Counts
56 → 56

prune778.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ x eps)) 2))
0.7b
(cbrt (* (cbrt (sin (/ eps 2))) (cbrt (sin (/ eps 2)))))
0.6b
(cbrt (cbrt (sin (/ eps 2))))
0.6b
(cbrt (sin (/ eps 2)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
13×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
Counts
4 → 45
Calls
4 calls:
Slowest
19.0ms
(sin (/ (+ x (+ x eps)) 2))
6.0ms
(cbrt (* (cbrt (sin (/ eps 2))) (cbrt (sin (/ eps 2)))))
3.0ms
(cbrt (cbrt (sin (/ eps 2))))
3.0ms
(cbrt (sin (/ eps 2)))

series609.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(cbrt (sin (/ eps 2)))
189.0ms
(cbrt (* (cbrt (sin (/ eps 2))) (cbrt (sin (/ eps 2)))))
165.0ms
(cbrt (cbrt (sin (/ eps 2))))
56.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify1.4s

Counts
57 → 57

prune918.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

regimes302.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch239.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.0s4472×body1280valid
1.8s650×body2560valid
1.4s1860×body640valid
810.0ms645×body320valid
77.0ms299×body160valid
9.0ms74×body80valid