Details

Time bar (total: 18.7s)

sample79.0ms

Algorithm
intervals
Results
40.0ms82×body1280valid
12.0ms180×body80valid
11.0ms32×body640valid
7.0ms26×body320valid
2.0ms14×body160valid

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize20.0ms

Local error

Found 2 expressions with local error:

4.1b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity
21×times-frac
14×add-cube-cbrt
10×difference-of-squares
7×associate-/l*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-- insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
2 calls:
Slowest
33.0ms
(/ (- (exp x) 1) x)
16.0ms
(- (exp x) 1)

series92.0ms

Calls
2 calls:
Slowest
67.0ms
(/ (- (exp x) 1) x)
24.0ms
(- (exp x) 1)

simplify1.9s

Calls
67 calls:
Slowest
229.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
225.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
164.0ms
(* -1 (/ (- 1 (exp x)) x))
84.0ms
(- (pow (exp x) 3) (pow 1 3))
54.0ms
(/ (- (sqrt (exp x)) (sqrt 1)) x)

prune495.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(* 1/6 x)
0.1b
(* x (+ (* 1/6 x) 1/2))
0.0b
(+ (* 1/6 x) 1/2)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×add-log-exp
3×insert-posit16
2×flip3-+ pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Calls
3 calls:
Slowest
21.0ms
(* x (+ (* 1/6 x) 1/2))
15.0ms
(+ (* 1/6 x) 1/2)
5.0ms
(* 1/6 x)

series161.0ms

Calls
3 calls:
Slowest
90.0ms
(* x (+ (* 1/6 x) 1/2))
44.0ms
(+ (* 1/6 x) 1/2)
27.0ms
(* 1/6 x)

simplify1.0s

Calls
33 calls:
Slowest
229.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
202.0ms
(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
200.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
66.0ms
(* (exp (* 1/6 x)) (exp 1/2))
65.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune410.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

4.1b
(log (/ (exp (exp x)) E))
0.0b
(/ (log (/ (exp (exp x)) E)) x)
0.0b
(/ (exp (exp x)) E)
0.0b
(exp (exp x))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
29×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×log-prod
9×pow1 add-exp-log
8×add-cbrt-cube
7×associate-/l*
6×associate-/r*
5×div-exp log-pow add-log-exp
4×insert-posit16
3×exp-prod rem-log-exp div-inv
2×cbrt-undiv log-div e-exp-1 clear-num frac-2neg
1×div-sub rem-exp-log
Calls
4 calls:
Slowest
23.0ms
(/ (log (/ (exp (exp x)) E)) x)
15.0ms
(/ (exp (exp x)) E)
7.0ms
(log (/ (exp (exp x)) E))
6.0ms
(exp (exp x))

series521.0ms

Calls
4 calls:
Slowest
250.0ms
(/ (log (/ (exp (exp x)) E)) x)
161.0ms
(log (/ (exp (exp x)) E))
76.0ms
(/ (exp (exp x)) E)
33.0ms
(exp (exp x))

simplify3.0s

Calls
89 calls:
Slowest
505.0ms
(/ (* (* (exp (exp x)) (exp (exp x))) (exp (exp x))) (* (* E E) E))
253.0ms
(/ (* (* (log (/ (exp (exp x)) E)) (log (/ (exp (exp x)) E))) (log (/ (exp (exp x)) E))) (* (* x x) x))
212.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
137.0ms
(log (/ (* (cbrt (exp (exp x))) (cbrt (exp (exp x)))) (* (cbrt E) (cbrt E))))
131.0ms
(+ (* (pow x 2) E) (+ E (* x E)))

prune900.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

4.1b
(+ -1 (* (exp x) (exp x)))
0.0b
(/ (+ -1 (* (exp x) (exp x))) (* x (+ (exp x) 1)))
0.0b
(* (exp x) (exp x))
0.0b
(* x (+ (exp x) 1))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×exp-prod add-cube-cbrt
13×pow1 add-cbrt-cube
11×add-exp-log
7×associate-*r*
6×associate-*l* add-log-exp
5×pow-prod-down
4×flip3-+ associate-*r/ pow-sqr pow-prod-up flip-+ insert-posit16
3×times-frac swap-sqr prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp associate-/r/ *-commutative unswap-sqr associate-/l/
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in pow-plus div-inv distribute-lft-out
Calls
4 calls:
Slowest
38.0ms
(* x (+ (exp x) 1))
30.0ms
(/ (+ -1 (* (exp x) (exp x))) (* x (+ (exp x) 1)))
12.0ms
(* (exp x) (exp x))
9.0ms
(+ -1 (* (exp x) (exp x)))

series182.0ms

Calls
4 calls:
Slowest
94.0ms
(/ (+ -1 (* (exp x) (exp x))) (* x (+ (exp x) 1)))
40.0ms
(* x (+ (exp x) 1))
29.0ms
(+ -1 (* (exp x) (exp x)))
18.0ms
(* (exp x) (exp x))

simplify6.3s

Calls
83 calls:
Slowest
647.0ms
(* (* (* x x) x) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
624.0ms
(/ (- (pow (exp x) 2) 1) (* x (+ (exp x) 1)))
472.0ms
(- (* -1 -1) (* (* (exp x) (exp x)) (* (exp x) (exp x))))
459.0ms
(/ (* (* (+ -1 (* (exp x) (exp x))) (+ -1 (* (exp x) (exp x)))) (+ -1 (* (exp x) (exp x)))) (* (* (* x (+ (exp x) 1)) (* x (+ (exp x) 1))) (* x (+ (exp x) 1))))
376.0ms
(/ (* (* (+ -1 (* (exp x) (exp x))) (+ -1 (* (exp x) (exp x)))) (+ -1 (* (exp x) (exp x)))) (* (* (* x x) x) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1))))

prune682.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes111.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.2b

bsearch59.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s2349×body1280valid
487.0ms1541×body640valid
402.0ms5462×body80valid
208.0ms884×body320valid
50.0ms399×body160valid