Details

Time bar (total: 23.5s)

sample249.0ms

Algorithm
intervals
Results
144.0ms106×body1280valid
42.0ms71×body640valid
37.0ms21×body2560valid
5.0ms15×body320valid
4.0ms32×body80valid
3.0ms11×body160valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (sin (+ x eps)) (sin x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize13.0ms

Local error

Found 2 expressions with local error:

2.6b
(sin (+ x eps))
1.1b
(- (sin (+ x eps)) (sin x))

rewrite43.0ms

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
36.0ms
(- (sin (+ x eps)) (sin x))
7.0ms
(sin (+ x eps))

series82.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
49.0ms
(- (sin (+ x eps)) (sin x))
33.0ms
(sin (+ x eps))

simplify818.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
404.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
195.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
80.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
57.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
14.0ms
(- (sin (+ x eps)) (sin x))

prune316.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize25.0ms

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))

rewrite60.0ms

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
32.0ms
(cos (/ (+ x (+ eps x)) 2))
14.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
14.0ms
(+ x (+ eps x))

series145.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
82.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
34.0ms
(cos (/ (+ x (+ eps x)) 2))
29.0ms
(+ x (+ eps x))

simplify1.5s

Counts
23 → 52
Calls
23 calls:
Slowest
386.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
324.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
213.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
64.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
61.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune564.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 59
Calls
4 calls:
Slowest
68.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
42.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
38.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
31.0ms
(cos (/ (+ x (+ eps x)) 2))

series256.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
75.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify2.3s

Counts
36 → 71
Calls
36 calls:
Slowest
399.0ms
(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
299.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
253.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
184.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
159.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune855.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.6b

localize56.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(pow E (cos (/ (+ x (+ eps x)) 2)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×add-exp-log
7×pow1 log-prod
6×unpow-prod-down add-cbrt-cube
4×rem-log-exp associate-*l* pow-exp insert-posit16 add-log-exp
3×pow-unpow associate-*r*
2×pow-to-exp e-exp-1 log-pow sqr-pow
1×pow-pow pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 67
Calls
4 calls:
Slowest
82.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
80.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
42.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
39.0ms
(cos (/ (+ x (+ eps x)) 2))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
103.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
76.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
44.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify7.1s

Counts
42 → 79
Calls
42 calls:
Slowest
720.0ms
(log (pow (* (cbrt E) (cbrt E)) (cos (/ (+ x (+ eps x)) 2))))
464.0ms
(log (pow (sqrt E) (cos (/ (+ x (+ eps x)) 2))))
459.0ms
(* (sqrt (log (pow E (cos (/ (+ x (+ eps x)) 2))))) (sqrt (sin (/ eps 2))))
450.0ms
(log (pow E (/ (cos (/ (+ x (+ eps x)) 2)) 2)))
416.0ms
(+ (log (log (pow E (cos (/ (+ x (+ eps x)) 2))))) (log (sin (/ eps 2))))

prune800.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.6b

regimes207.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.1b

bsearch176.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.2s3227×body1280valid
1.5s1967×body640valid
1.4s616×body2560valid
628.0ms764×body320valid
125.0ms1075×body80valid
85.0ms351×body160valid