Details

Time bar (total: 24.3s)

sample219.0ms

Algorithm
intervals
Results
130.0ms133×body1280valid
40.0ms75×body640valid
25.0ms16×body2560valid
8.0ms22×body320valid
2.0ms8×body160valid
0.0ms2×body80valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize13.0ms

Local error

Found 2 expressions with local error:

4.4b
(cos (+ x eps))
0.8b
(- (cos (+ x eps)) (cos x))

rewrite65.0ms

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
37.0ms
(cos (+ x eps))
26.0ms
(- (cos (+ x eps)) (cos x))

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
70.0ms
(- (cos (+ x eps)) (cos x))
27.0ms
(cos (+ x eps))

simplify2.0s

Counts
33 → 48
Calls
33 calls:
Slowest
225.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
187.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
168.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
168.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
159.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune469.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b
(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))))

rewrite133.0ms

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
56.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
41.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
23.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

series354.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
134.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
42.0ms
(+ x (+ eps x))
40.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify3.4s

Counts
38 → 87
Calls
38 calls:
Slowest
696.0ms
(* (* (* -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)))))
606.0ms
(* (* (* -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)))))
434.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
298.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
230.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))

prune971.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.6b

localize36.0ms

Local error

Found 3 expressions with local error:

4.4b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-log-exp
5×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u sum-log fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative associate-+r+ flip3-+ associate-*l* *-commutative flip-+
Counts
3 → 52
Calls
3 calls:
Slowest
54.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
24.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(+ x (+ eps x))

series207.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
141.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
36.0ms
(+ x (+ eps x))
30.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.1s

Counts
24 → 61
Calls
24 calls:
Slowest
578.0ms
(* (* (* (* -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))))
535.0ms
(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
238.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
192.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
64.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune631.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize68.0ms

Local error

Found 4 expressions with local error:

4.4b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.2b
(log1p (expm1 (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))))
0.1b
(expm1 (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
1×log1p-udef expm1-log1p associate-*l* log1p-expm1 *-commutative expm1-udef
Counts
4 → 55
Calls
4 calls:
Slowest
73.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
39.0ms
(sin (/ (+ x (+ eps x)) 2))
0.0ms
(expm1 (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))))
0.0ms
(log1p (expm1 (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))))

series654.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(log1p (expm1 (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))))
227.0ms
(expm1 (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))))
156.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
36.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify3.6s

Counts
23 → 67
Calls
23 calls:
Slowest
589.0ms
(* (* (* (* -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))))
542.0ms
(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
425.0ms
(- (exp (* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))) 1)
419.0ms
(- (exp (* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))) 1)
310.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune795.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.6b

regimes219.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.2b

bsearch135.0ms

end0.0ms

sample7.9s

Algorithm
intervals
Results
4.0s4462×body1280valid
1.8s619×body2560valid
1.3s1908×body640valid
358.0ms676×body320valid
100.0ms264×body160valid
8.0ms71×body80valid