Details

Time bar (total: 17.8s)

sample92.0ms

Algorithm
intervals
Results
45.0ms79×body1280valid
19.0ms51×body640valid
12.0ms163×body80valid
6.0ms24×body320valid
2.0ms12×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(/ (- (exp x) 1) x)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize15.0ms

Local error

Found 2 expressions with local error:

3.1b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite46.0ms

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
29.0ms
(/ (- (exp x) 1) x)
16.0ms
(- (exp x) 1)

series69.0ms

Calls
2 calls:
Slowest
54.0ms
(/ (- (exp x) 1) x)
15.0ms
(- (exp x) 1)

simplify2.1s

Calls
67 calls:
Slowest
272.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
220.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
132.0ms
(* -1 (/ (- 1 (exp x)) x))
83.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
78.0ms
(/ (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))) (* (cbrt x) (cbrt x)))

prune450.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
2×pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod insert-posit16 add-log-exp unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+
Calls
2 calls:
Slowest
31.0ms
(* x (+ (* 1/6 x) 1/2))
8.0ms
(* 1/6 x)

series116.0ms

Calls
2 calls:
Slowest
90.0ms
(* x (+ (* 1/6 x) 1/2))
26.0ms
(* 1/6 x)

simplify978.0ms

Calls
29 calls:
Slowest
280.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
196.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
183.0ms
(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
52.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
47.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune335.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.0b
(+ -1 (* (exp x) (exp x)))
0.0b
(/ (+ -1 (* (exp x) (exp x))) (* x (+ (exp x) 1)))
0.0b
(* (exp x) (exp x))
0.0b
(+ (exp x) 1)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt exp-prod *-un-lft-identity
16×add-cube-cbrt
11×pow1 add-cbrt-cube
9×add-exp-log
8×add-log-exp
4×flip3-+ pow-prod-down pow-sqr pow-prod-up flip-+ insert-posit16
3×times-frac swap-sqr associate-*r* associate-*l* associate-/l*
2×cbrt-undiv +-commutative sum-log div-exp prod-exp associate-*r/ associate-/r/ cbrt-unprod associate-/l/
1×pow2 clear-num associate-/r* frac-2neg pow-plus *-commutative div-inv distribute-lft-out unswap-sqr
Calls
4 calls:
Slowest
50.0ms
(/ (+ -1 (* (exp x) (exp x))) (* x (+ (exp x) 1)))
25.0ms
(* (exp x) (exp x))
13.0ms
(+ (exp x) 1)
9.0ms
(+ -1 (* (exp x) (exp x)))

series173.0ms

Calls
4 calls:
Slowest
99.0ms
(/ (+ -1 (* (exp x) (exp x))) (* x (+ (exp x) 1)))
44.0ms
(+ -1 (* (exp x) (exp x)))
15.0ms
(* (exp x) (exp x))
14.0ms
(+ (exp x) 1)

simplify4.7s

Calls
70 calls:
Slowest
491.0ms
(/ (* (* (+ -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))))
463.0ms
(- (* -1 -1) (* (* (exp x) (exp x)) (* (exp x) (exp x))))
386.0ms
(/ (* (* (+ -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))))
386.0ms
(+ (pow -1 3) (pow (* (exp x) (exp x)) 3))
267.0ms
(/ (- (pow (exp x) 2) 1) (* x (+ (exp x) 1)))

prune661.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

3.1b
(- (exp x) 1)
3.0b
(log (exp (- (exp x) 1)))
0.0b
(/ (log (exp (- (exp x) 1))) x)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
43×*-un-lft-identity
40×log-pow
35×exp-prod
33×times-frac
25×add-cube-cbrt
12×difference-of-squares
11×associate-/l*
8×pow1
6×difference-of-sqr-1 distribute-lft-out--
5×log-prod add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* insert-posit16
2×log-div sub-neg exp-diff exp-sum
1×cbrt-undiv clear-num frac-2neg flip3-- diff-log div-sub div-exp rem-log-exp div-inv flip--
Calls
3 calls:
Slowest
74.0ms
(/ (log (exp (- (exp x) 1))) x)
25.0ms
(log (exp (- (exp x) 1)))
8.0ms
(- (exp x) 1)

series99.0ms

Calls
3 calls:
Slowest
49.0ms
(/ (log (exp (- (exp x) 1))) x)
25.0ms
(log (exp (- (exp x) 1)))
25.0ms
(- (exp x) 1)

simplify3.9s

Calls
110 calls:
Slowest
247.0ms
(/ (* (* (log (exp (- (exp x) 1))) (log (exp (- (exp x) 1)))) (log (exp (- (exp x) 1)))) (* (* x x) x))
229.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
212.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
211.0ms
(/ (log (exp (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))) (cbrt x))
174.0ms
(/ (log (exp (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))) (sqrt x))

prune851.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch21.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s2231×body1280valid
538.0ms1653×body640valid
403.0ms5494×body80valid
171.0ms845×body320valid
58.0ms427×body160valid