Details

Time bar (total: 23.2s)

sample241.0ms

Algorithm
intervals
Results
106.0ms105×body1280valid
64.0ms18×body2560valid
39.0ms64×body640valid
9.0ms20×body320valid
6.0ms39×body80valid
3.0ms10×body160valid

simplify17.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (sin (+ x eps)) (sin x))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize27.0ms

Local error

Found 2 expressions with local error:

3.8b
(sin (+ x eps))
0.6b
(- (sin (+ x eps)) (sin x))

rewrite82.0ms

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
67.0ms
(- (sin (+ x eps)) (sin x))
14.0ms
(sin (+ x eps))

series79.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(- (sin (+ x eps)) (sin x))
21.0ms
(sin (+ x eps))

simplify2.2s

Counts
33 → 48
Calls
33 calls:
Slowest
255.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
223.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
200.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
181.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
172.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune451.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

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
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
39.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
22.0ms
(+ x (+ eps x))
19.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
79.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
32.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(+ x (+ eps x))

simplify3.7s

Counts
37 → 85
Calls
37 calls:
Slowest
643.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
637.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
540.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
401.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
359.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))

prune933.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ x (+ eps x)) 2))
4.0b
(cos (/ (+ x (+ eps x)) 2))
4.0b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite137.0ms

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
42.0ms
(cos (/ (+ x (+ eps x)) 2))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
35.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
30.0ms
(cos (/ (+ x (+ eps x)) 2))
27.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts
15 → 56
Calls
15 calls:
Slowest
462.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
461.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
431.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
381.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
114.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune692.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ x (+ eps x)) 2))
4.0b
(cos (/ (+ x (+ eps x)) 2))
4.0b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite101.0ms

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
39.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cos (/ (+ x (+ eps x)) 2))
20.0ms
(cos (/ (+ x (+ eps x)) 2))
18.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
42.0ms
(cos (/ (+ x (+ eps x)) 2))
35.0ms
(cos (/ (+ x (+ eps x)) 2))
28.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
27.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.1s

Counts
15 → 56
Calls
15 calls:
Slowest
444.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
422.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
401.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
324.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
68.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune903.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes203.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.3b

bsearch253.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.3s3332×body1280valid
1.5s1806×body640valid
1.3s606×body2560valid
396.0ms761×body320valid
151.0ms1131×body80valid
104.0ms364×body160valid