Details

Time bar (total: 24.9s)

sample235.0ms

Algorithm
intervals
Results
122.0ms113×body1280valid
45.0ms66×body640valid
36.0ms18×body2560valid
13.0ms26×body320valid
4.0ms12×body160valid
3.0ms21×body80valid

simplify16.0ms

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

prune55.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize31.0ms

Local error

Found 2 expressions with local error:

5.8b
(sin (+ x eps))
1.5b
(- (sin (+ x eps)) (sin x))

rewrite80.0ms

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
64.0ms
(- (sin (+ x eps)) (sin x))
15.0ms
(sin (+ x eps))

series96.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
54.0ms
(- (sin (+ x eps)) (sin x))
42.0ms
(sin (+ x eps))

simplify2.0s

Counts
33 → 48
Calls
33 calls:
Slowest
242.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
192.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
181.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
167.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
156.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))

prune451.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

5.6b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sum-log fma-def distribute-lft-out
2×*-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
29.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
29.0ms
(cos (/ (+ x (+ eps x)) 2))
11.0ms
(+ x (+ eps x))
10.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
94.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
46.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(+ x (+ eps x))

simplify3.3s

Counts
37 → 85
Calls
37 calls:
Slowest
685.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
553.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
439.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
396.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
207.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune855.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

5.6b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.3b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite210.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 67
Calls
4 calls:
Slowest
91.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
48.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
36.0ms
(cos (/ (+ x (+ eps x)) 2))
35.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
50.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
27.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.8s

Counts
36 → 79
Calls
36 calls:
Slowest
463.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
430.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
379.0ms
(* (* (* (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))))
257.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
208.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))

prune957.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize64.0ms

Local error

Found 4 expressions with local error:

5.6b
(cos (/ (+ x (+ eps x)) 2))
5.6b
(cos (/ (+ x (+ eps x)) 2))
0.8b
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
0.8b
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod log-pow
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 sqrt-pow1
6×exp-prod add-exp-log sqrt-prod
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow1/2 rem-log-exp
Counts
4 → 66
Calls
4 calls:
Slowest
54.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
51.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
24.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cos (/ (+ x (+ eps x)) 2))

series278.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
93.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
44.0ms
(cos (/ (+ x (+ eps x)) 2))
43.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts
34 → 78
Calls
34 calls:
Slowest
451.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
340.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
280.0ms
(- (log (sqrt E)) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
267.0ms
(- (log (sqrt E)) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
61.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes152.0ms

Accuracy

95.1% (0.7b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 15.0b

bsearch239.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
5.1s3347×body1280valid
1.4s1795×body640valid
1.2s644×body2560valid
359.0ms739×body320valid
144.0ms1100×body80valid
105.0ms375×body160valid