Details

Time bar (total: 20.9s)

sample232.0ms

Algorithm
intervals
Results
101.0ms103×body1280valid
74.0ms70×body640valid
27.0ms16×body2560valid
12.0ms25×body320valid
5.0ms35×body80valid
2.0ms7×body160valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(- (sin (+ x eps)) (sin x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize15.0ms

Local error

Found 2 expressions with local error:

4.3b
(sin (+ x eps))
1.0b
(- (sin (+ x eps)) (sin x))

rewrite74.0ms

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
66.0ms
(- (sin (+ x eps)) (sin x))
7.0ms
(sin (+ x eps))

series105.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
72.0ms
(- (sin (+ x eps)) (sin x))
32.0ms
(sin (+ x eps))

simplify2.1s

Counts
33 → 48
Calls
33 calls:
Slowest
215.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
208.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
205.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
177.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
168.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune428.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize24.0ms

Local error

Found 3 expressions with local error:

4.5b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite87.0ms

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
40.0ms
(cos (/ (+ x (+ eps x)) 2))
23.0ms
(+ x (+ eps x))
23.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series132.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
75.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
32.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(+ x (+ eps x))

simplify1.5s

Counts
25 → 61
Calls
25 calls:
Slowest
415.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
405.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
214.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
49.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
47.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune682.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize34.0ms

Local error

Found 4 expressions with local error:

4.5b
(cos (/ (+ x (+ eps x)) 2))
4.5b
(cos (/ (+ x (+ eps x)) 2))
4.5b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Counts
4 → 44
Calls
4 calls:
Slowest
47.0ms
(cos (/ (+ x (+ eps x)) 2))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
38.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series145.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
42.0ms
(cos (/ (+ x (+ eps x)) 2))
39.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
37.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.4s

Counts
15 → 56
Calls
15 calls:
Slowest
551.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
463.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
452.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
409.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
87.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune740.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize70.0ms

Local error

Found 4 expressions with local error:

4.5b
(cos (/ (+ x (+ eps x)) 2))
4.5b
(cos (/ (+ x (+ eps x)) 2))
4.5b
(cos (/ (+ x (+ eps x)) 2))
4.5b
(cos (/ (+ x (+ eps x)) 2))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
Slowest
38.0ms
(cos (/ (+ x (+ eps x)) 2))
36.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cos (/ (+ x (+ eps x)) 2))
20.0ms
(cos (/ (+ x (+ eps x)) 2))

series168.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(cos (/ (+ x (+ eps x)) 2))
42.0ms
(cos (/ (+ x (+ eps x)) 2))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
41.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.2s

Counts
12 → 52
Calls
12 calls:
Slowest
488.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
447.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
429.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
417.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
66.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune904.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.6b

regimes224.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.2b

bsearch104.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.2s3319×body1280valid
1.6s619×body2560valid
1.5s1876×body640valid
360.0ms760×body320valid
143.0ms1081×body80valid
130.0ms345×body160valid