Details

Time bar (total: 24.5s)

sample196.0ms

Algorithm
intervals
Results
97.0ms134×body1280valid
43.0ms69×body640valid
35.0ms23×body2560valid
8.0ms21×body320valid
1.0ms4×body160valid
1.0ms5×body80valid

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(- (cos (+ x eps)) (cos x))

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize25.0ms

Local error

Found 2 expressions with local error:

4.2b
(cos (+ x eps))
1.0b
(- (cos (+ x eps)) (cos x))

rewrite40.0ms

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 cos-sum add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 42
Calls
2 calls:
Slowest
24.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

series102.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
74.0ms
(- (cos (+ x eps)) (cos x))
28.0ms
(cos (+ x eps))

simplify2.2s

Counts
33 → 48
Calls
33 calls:
Slowest
223.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
205.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
184.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
177.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
163.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune538.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

4.0b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite150.0ms

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 sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 75
Calls
4 calls:
Slowest
57.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
52.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
29.0ms
(sin (/ (+ x (+ eps x)) 2))
11.0ms
(+ x (+ eps x))

series323.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
118.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
38.0ms
(sin (/ (+ x (+ eps x)) 2))
30.0ms
(+ x (+ eps x))

simplify3.2s

Counts
38 → 87
Calls
38 calls:
Slowest
609.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
562.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
400.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
319.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
257.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

4.0b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.3b
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.2b
(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite41.0ms

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
27.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
1.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
74.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
59.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
35.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.1s

Counts
24 → 67
Calls
24 calls:
Slowest
379.0ms
(* (* (* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
302.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
299.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
284.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
90.0ms
(+ x (+ (* 1/2 (pow x 2)) (* 1/2 eps)))

prune900.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize50.0ms

Local error

Found 4 expressions with local error:

4.0b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.3b
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.2b
(expm1 (log1p (* (log1p (expm1 (sin (/ (+ 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
4×expm1-log1p-u insert-posit16 log1p-expm1-u 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
25.0ms
(sin (/ (+ x (+ eps x)) 2))
16.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.0ms
(expm1 (log1p (* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))))
0.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series626.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
289.0ms
(expm1 (log1p (* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))))
188.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
103.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
46.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.2s

Counts
24 → 67
Calls
24 calls:
Slowest
378.0ms
(* (* (* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
316.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
315.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
294.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
253.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune962.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

regimes297.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch265.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.0s4484×body1280valid
1.5s646×body2560valid
1.3s1826×body640valid
271.0ms676×body320valid
156.0ms293×body160valid
10.0ms75×body80valid