Details

Time bar (total: 35.3s)

sample257.0ms

Algorithm
intervals
Results
154.0ms142×body1280valid
36.0ms58×body640valid
35.0ms18×body2560valid
15.0ms27×body320valid
3.0ms11×body160valid

simplify18.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
18.0ms
(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize26.0ms

Local error

Found 2 expressions with local error:

2.9b
(cos (+ x eps))
0.8b
(- (cos (+ x eps)) (cos 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 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
45.0ms
(cos (+ x eps))
28.0ms
(- (cos (+ x eps)) (cos x))

series105.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
77.0ms
(- (cos (+ x eps)) (cos x))
28.0ms
(cos (+ x eps))

simplify3.3s

Counts
61 → 48
Calls
61 calls:
Slowest
451.0ms
(* (* (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)))
260.0ms
(- (pow (cos (+ x eps)) 3) (pow (cos x) 3))
214.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
209.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
189.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))

prune522.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

2.9b
(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))))

rewrite197.0ms

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
89.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
61.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
24.0ms
(+ x (+ eps x))
21.0ms
(sin (/ (+ x (+ eps x)) 2))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
123.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
39.0ms
(+ x (+ eps x))
32.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify7.2s

Counts
84 → 87
Calls
84 calls:
Slowest
698.0ms
(* (* (* -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)))))
675.0ms
(* (* (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))) (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
485.0ms
(* (* (* -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)))))
418.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
369.0ms
(+ (* x x) (- (* (+ eps x) (+ eps x)) (* x (+ eps x))))

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 3 expressions with local error:

2.9b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite117.0ms

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
80.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
24.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

series205.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
122.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
54.0ms
(sin (/ (+ x (+ eps x)) 2))
28.0ms
(+ x (+ eps x))

simplify5.0s

Counts
58 → 61
Calls
58 calls:
Slowest
582.0ms
(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))) (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))) (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))))
557.0ms
(* (* (* (* -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))))
556.0ms
(* (* (* (* -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))))
408.0ms
(+ (* x x) (- (* (+ eps x) (+ eps x)) (* x (+ eps x))))
309.0ms
(exp (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2))))

prune734.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

2.9b
(sin (/ (+ x (+ eps x)) 2))
0.4b
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.3b
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.2b
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×insert-posit16 log1p-expm1-u 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
48.0ms
(sin (/ (+ x (+ eps x)) 2))
36.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
1.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
102.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
73.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
52.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify5.4s

Counts
64 → 67
Calls
64 calls:
Slowest
757.0ms
(* (* (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2))) (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))) (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2))))
604.0ms
(* (* (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
579.0ms
(* (* (* (* -2 -2) -2) (* (* (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
295.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
294.0ms
(exp (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2))))

prune780.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

regimes251.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 14.7b

bsearch273.0ms

end0.0ms

sample9.0s

Algorithm
intervals
Results
5.6s4387×body1280valid
1.4s689×body2560valid
1.2s1817×body640valid
400.0ms716×body320valid
76.0ms297×body160valid
12.0ms94×body80valid