Details

Time bar (total: 25.5s)

sample199.0ms

Algorithm
intervals
Results
98.0ms147×body1280valid
58.0ms16×body2560valid
27.0ms63×body640valid
5.0ms16×body320valid
2.0ms11×body160valid
0.0ms3×body80valid

simplify14.0ms

Calls
1 calls:
Slowest
14.0ms
(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize18.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (cos (+ x eps)) (cos x))
1.9b
(cos (+ x eps))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×cos-sum add-log-exp
3×fma-neg
2×associate--l- expm1-log1p-u pow1 +-commutative add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
13.0ms
(- (cos (+ x eps)) (cos x))
8.0ms
(cos (+ x eps))

series126.0ms

Calls
2 calls:
Slowest
99.0ms
(- (cos (+ x eps)) (cos x))
27.0ms
(cos (+ x eps))

simplify2.1s

Calls
35 calls:
Slowest
251.0ms
(- 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))))))
201.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
185.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
183.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune555.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

2.0b
(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))))

rewrite698.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×associate-*r*
16×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*l* add-log-exp
5×unswap-sqr
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sum-log fma-def *-commutative distribute-lft-out
2×+-commutative associate-+r+ sin-mult
1×flip3-+ associate-*r/ flip-+
Calls
4 calls:
Slowest
417.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
189.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
75.0ms
(sin (/ (+ x (+ eps x)) 2))
16.0ms
(+ x (+ eps x))

series310.0ms

Calls
4 calls:
Slowest
118.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
114.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms
(+ x (+ eps x))
37.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify4.1s

Calls
53 calls:
Slowest
588.0ms
(* (* (* -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)))))
575.0ms
(* (* (* -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)))))
512.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
320.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
306.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize62.0ms

Local error

Found 4 expressions with local error:

2.0b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.3b
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.2b
(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u log1p-expm1-u
4×insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×log1p-expm1
1×log1p-udef expm1-log1p pow-prod-down prod-exp *-commutative cbrt-unprod expm1-udef unswap-sqr
Calls
4 calls:
Slowest
63.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))

series323.0ms

Calls
4 calls:
Slowest
129.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
92.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
51.0ms
(sin (/ (+ x (+ eps x)) 2))
51.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))

simplify2.0s

Calls
25 calls:
Slowest
397.0ms
(* (* (* (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))))
291.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
262.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
224.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
86.0ms
(+ x (+ (* 1/2 (pow x 2)) (* 1/2 eps)))

prune802.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 3 expressions with local error:

2.0b
(sin (fma 1/2 eps x))
0.3b
(* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))
0.0b
(* -2 (* (sin (* eps 1/2)) (sin (fma 1/2 eps x))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt associate-*r*
10×pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*l* add-cube-cbrt
7×sin-sum fma-udef
5×distribute-rgt-in distribute-lft-in unswap-sqr
4×pow-prod-down prod-exp cbrt-unprod
3×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×sin-mult
1×associate-*r/
Calls
3 calls:
Slowest
107.0ms
(* -2 (* (sin (* eps 1/2)) (sin (fma 1/2 eps x))))
35.0ms
(* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))
2.0ms
(sin (fma 1/2 eps x))

series185.0ms

Calls
3 calls:
Slowest
83.0ms
(* -2 (* (sin (* eps 1/2)) (sin (fma 1/2 eps x))))
75.0ms
(* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))
26.0ms
(sin (fma 1/2 eps x))

simplify3.3s

Calls
51 calls:
Slowest
678.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (* eps 1/2)) (sin (fma 1/2 eps x))) (* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))) (* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))))
450.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (sin (fma 1/2 eps x)) (sin (fma 1/2 eps x))) (sin (fma 1/2 eps x)))))
343.0ms
(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (sin (fma 1/2 eps x)) (sin (fma 1/2 eps x))) (sin (fma 1/2 eps x))))
238.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
228.0ms
(- (+ x (* 1/2 eps)) (* 1/48 (pow eps 3)))

prune886.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes154.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.2s4550×body1280valid
1.3s606×body2560valid
1.3s1792×body640valid
331.0ms671×body320valid
129.0ms295×body160valid
11.0ms86×body80valid