Details

Time bar (total: 22.0s)

sample200.0ms

Algorithm
intervals
Results
98.0ms99×body1280valid
42.0ms72×body640valid
30.0ms17×body2560valid
11.0ms29×body320valid
3.0ms12×body160valid
3.0ms27×body80valid

simplify17.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
17.0ms
(- (sin (+ x eps)) (sin x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize38.0ms

Local error

Found 2 expressions with local error:

3.0b
(sin (+ x eps))
2.5b
(- (sin (+ x eps)) (sin x))

rewrite67.0ms

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
57.0ms
(- (sin (+ x eps)) (sin x))
9.0ms
(sin (+ x eps))

series92.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
68.0ms
(- (sin (+ x eps)) (sin x))
24.0ms
(sin (+ x eps))

simplify2.0s

Counts
33 → 48
Calls
33 calls:
Slowest
277.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
185.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
179.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
177.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
136.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune471.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 3 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite93.0ms

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
48.0ms
(cos (/ (+ x (+ eps x)) 2))
22.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
22.0ms
(+ x (+ eps x))

series190.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
122.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
42.0ms
(+ x (+ eps x))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.5s

Counts
25 → 61
Calls
25 calls:
Slowest
407.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
383.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
224.0ms
(- (* 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)))
57.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune668.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.6b

localize52.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.3b
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef unswap-sqr
Counts
4 → 55
Calls
4 calls:
Slowest
21.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
1.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
95.0ms
(expm1 (cos (/ (+ x (+ eps x)) 2)))
75.0ms
(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
46.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.5s

Counts
24 → 67
Calls
24 calls:
Slowest
444.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
414.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
384.0ms
(* (* (* (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
311.0ms
(- E (+ (* 1/2 (* x (* E eps))) (+ (* 1/2 (* (pow x 2) E)) 1)))
266.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune770.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize70.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
3.1b
(cos (/ (+ x (+ eps x)) 2))
3.1b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (cos (/ (+ x (+ eps x)) 2)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 44
Calls
4 calls:
Slowest
40.0ms
(cos (/ (+ x (+ eps x)) 2))
34.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cos (/ (+ x (+ eps x)) 2))
2.0ms
(cbrt (cos (/ (+ x (+ eps x)) 2)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(cbrt (cos (/ (+ x (+ eps x)) 2)))
42.0ms
(cos (/ (+ x (+ eps x)) 2))
37.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.7s

Counts
15 → 56
Calls
15 calls:
Slowest
465.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
461.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
444.0ms
(- 1 (+ (* 1/6 (* x eps)) (* 1/6 (pow x 2))))
343.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
283.0ms
(pow (cos (* 1/2 (+ (* 2 x) eps))) 1/3)

prune646.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.6b

regimes240.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.4b

bsearch273.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.4s3242×body1280valid
1.4s660×body2560valid
1.4s1866×body640valid
584.0ms1101×body80valid
435.0ms779×body320valid
136.0ms352×body160valid