Details

Time bar (total: 1.6m)

sample70.0ms

Algorithm
intervals
Results
22.0ms85×body10240exit
21.0ms71×body1280valid
12.0ms54×body640valid
4.0ms93×body80valid
3.0ms24×body320valid
2.0ms15×body160valid

simplify9.0ms

Calls
1 calls:
Slowest
9.0ms
(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize8.0ms

Local error

Found 2 expressions with local error:

3.9b
(- (exp x) 1)
0.3b
(/ (exp x) (- (exp x) 1))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×times-frac
11×*-un-lft-identity add-cube-cbrt
5×difference-of-sqr-1
4×associate-/r* add-cbrt-cube
3×add-exp-log associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- add-log-exp
1×cbrt-undiv clear-num sub-neg frac-2neg div-exp div-inv
Calls
2 calls:
Slowest
34.0ms
(/ (exp x) (- (exp x) 1))
3.0ms
(- (exp x) 1)

series37.0ms

Calls
2 calls:
Slowest
20.0ms
(/ (exp x) (- (exp x) 1))
17.0ms
(- (exp x) 1)

simplify1.2s

Calls
41 calls:
Slowest
422.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
127.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
83.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
63.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
30.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (- (exp x) 1)))

prune404.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b
(* 1/12 x)
0.0b
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
2×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×+-commutative associate-+r+ sum-log flip3-+ *-commutative flip-+
Calls
2 calls:
Slowest
14.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0ms
(* 1/12 x)

series17.0ms

Calls
2 calls:
Slowest
10.0ms
(* 1/12 x)
7.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

simplify139.0ms

Calls
7 calls:
Slowest
63.0ms
(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
23.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
23.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
21.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
3.0ms
(* 1/12 x)

prune162.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (pow (exp x) 3) (pow 1 3))
0.3b
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
0.2b
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b
(pow (exp x) 3)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
208×add-sqr-sqrt
157×*-un-lft-identity
106×add-cube-cbrt
51×difference-of-squares
36×associate-/r*
34×distribute-lft-out--
20×unpow-prod-down cube-prod
18×cube-mult
17×difference-cubes
12×add-cbrt-cube associate-/l*
11×associate-/r/
9×add-exp-log
6×div-inv add-log-exp
5×pow1 flip3-+ flip-+
4×cbrt-undiv div-exp insert-posit16
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow diff-log unpow3 div-sub pow-exp rem-cube-cbrt
Calls
4 calls:
Slowest
37.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
24.0ms
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
15.0ms
(- (pow (exp x) 3) (pow 1 3))
2.0ms
(pow (exp x) 3)

series151.0ms

Calls
4 calls:
Slowest
58.0ms
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
53.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
26.0ms
(- (pow (exp x) 3) (pow 1 3))
14.0ms
(pow (exp x) 3)

simplify51.4s

Calls
340 calls:
Slowest
766.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (/ (- (pow (exp x) 3) (pow 1 3)) (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))))))
717.0ms
(/ (* (+ (pow (exp x) 2) (+ (exp x) 1)) (exp x)) (- (pow (exp x) 3) 1))
698.0ms
(/ (* (+ (pow (exp x) 2) (+ (exp x) 1)) (exp x)) (- (pow (exp x) 3) 1))
667.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (/ (* (* (- (pow (exp x) 3) (pow 1 3)) (- (pow (exp x) 3) (pow 1 3))) (- (pow (exp x) 3) (pow 1 3))) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
568.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (/ 1 (* (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))))

prune2.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize98.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (exp x) (* (exp x) (exp x)))
3.8b
(+ (exp (+ (+ x x) x)) -1)
0.3b
(* (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))) (/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))))
0.3b
(/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))))

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
48×times-frac
46×associate-*r*
45×flip3-+ flip-+
38×add-exp-log
37×*-un-lft-identity
36×associate-/r/ add-cube-cbrt
32×frac-sub
29×add-cbrt-cube
27×cbrt-prod
25×frac-times
16×prod-exp cbrt-unprod
15×associate-*l/
14×difference-of-squares
13×associate-*r/
9×pow1 cbrt-undiv div-exp
6×associate-/l* add-log-exp
4×associate-/r* insert-posit16
3×flip3-- pow-prod-down flip--
2×div-inv
1×+-commutative difference-of-sqr--1 clear-num sub-neg frac-2neg distribute-rgt-out-- diff-log associate-*l* *-commutative
Calls
4 calls:
Slowest
387.0ms
(* (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))) (/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))))
61.0ms
(/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))))
34.0ms
(+ (exp (+ (+ x x) x)) -1)
4.0ms
(- (exp x) (* (exp x) (exp x)))

series515.0ms

Calls
4 calls:
Slowest
240.0ms
(* (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))) (/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))))
230.0ms
(/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))))
32.0ms
(- (exp x) (* (exp x) (exp x)))
13.0ms
(+ (exp (+ (+ x x) x)) -1)

simplify35.8s

Calls
176 calls:
Slowest
1.5s
(* (* (* (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))) (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1)))))) (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1)))))) (/ (exp x) (* (* (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))))))
788.0ms
(* (* (+ (exp (+ (+ x x) x)) -1) (+ (* (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x)))) (- (* (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1)))) (* (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))))
650.0ms
(/ (exp x) (* (* (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))))
561.0ms
(* (+ (exp (+ (+ x x) x)) -1) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))))
544.0ms
(* (* (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))) (+ (* (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x))))) (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))))

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes54.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 21.2b

bsearch35.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
857.0ms2225×body1280valid
629.0ms2582×body10240exit
378.0ms1685×body640valid
141.0ms2855×body80valid
103.0ms821×body320valid
52.0ms418×body160valid