Details

Time bar (total: 17.4s)

sample84.0ms

Algorithm
intervals
Results
35.0ms71×body1280valid
16.0ms48×body640valid
13.0ms178×body80valid
6.0ms27×body320valid
2.0ms12×body160valid

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
46.0ms
(/ (- (exp x) 1) x)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize13.0ms

Local error

Found 2 expressions with local error:

3.3b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite27.0ms

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
Counts
2 → 64
Calls
2 calls:
Slowest
17.0ms
(/ (- (exp x) 1) x)
8.0ms
(- (exp x) 1)

series93.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
69.0ms
(/ (- (exp x) 1) x)
24.0ms
(- (exp x) 1)

simplify1.8s

Counts
67 → 70
Calls
67 calls:
Slowest
228.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
186.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
126.0ms
(* -1 (/ (- 1 (exp x)) x))
84.0ms
(- (pow (exp x) 3) (pow 1 3))
58.0ms
(/ (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))) (* (cbrt x) (cbrt x)))

prune508.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

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-+
Counts
2 → 42
Calls
2 calls:
Slowest
42.0ms
(* x (+ (* 1/6 x) 1/2))
11.0ms
(* 1/6 x)

series104.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
77.0ms
(* x (+ (* 1/6 x) 1/2))
27.0ms
(* 1/6 x)

simplify1.3s

Counts
29 → 48
Calls
29 calls:
Slowest
598.0ms
(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
222.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
219.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
45.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
35.0ms
(* x (+ (* 1/6 x) 1/2))

prune361.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b
(+ (exp (+ x (+ x x))) -1)
0.0b
(exp (+ x (+ x x)))
0.0b
(* (exp x) (exp x))
0.0b
(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

rewrite580.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
30×exp-prod
28×add-sqr-sqrt
20×add-cube-cbrt
12×add-log-exp
11×pow1 add-cbrt-cube distribute-lft-out
9×add-exp-log
5×times-frac associate-/l*
4×sum-log pow-prod-down distribute-rgt1-in pow-sqr pow-prod-up insert-posit16
3×difference-of-sqr--1 flip3-+ distribute-rgt-out swap-sqr associate-*r* associate-*l* flip-+ rem-exp-log
2×cbrt-undiv distribute-lft1-in div-exp prod-exp associate-*r/ associate-/r/ cbrt-unprod associate-/l/
1×pow2 +-commutative clear-num associate-/r* frac-2neg pow-plus exp-sum *-commutative div-inv unswap-sqr
Counts
4 → 103
Calls
4 calls:
Slowest
389.0ms
(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
128.0ms
(+ (exp (+ x (+ x x))) -1)
36.0ms
(exp (+ x (+ x x)))
24.0ms
(* (exp x) (exp x))

series173.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
29.0ms
(+ (exp (+ x (+ x x))) -1)
14.0ms
(* (exp x) (exp x))
9.0ms
(exp (+ x (+ x x)))

simplify6.6s

Counts
91 → 115
Calls
91 calls:
Slowest
815.0ms
(/ (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)) (* (* (* x x) x) (* (* (+ (* (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))))))
748.0ms
(/ (* (* (+ (exp (+ x (+ x x))) -1) (+ (exp (+ x (+ x x))) -1)) (+ (exp (+ x (+ x x))) -1)) (* (* (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
406.0ms
(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))
358.0ms
(+ (pow (exp (+ x (+ x x))) 3) (pow -1 3))
325.0ms
(+ (* (* (exp x) (exp x)) (* (exp x) (exp x))) (- (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))) (* (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

3.3b
(+ (exp x) -1)
0.0b
(/ (+ (exp x) -1) x)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
17×add-sqr-sqrt
15×times-frac
12×add-cube-cbrt
5×difference-of-sqr--1 distribute-lft-out associate-/l*
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-+ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
2 → 52
Calls
2 calls:
Slowest
26.0ms
(/ (+ (exp x) -1) x)
7.0ms
(+ (exp x) -1)

series90.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
62.0ms
(/ (+ (exp x) -1) x)
28.0ms
(+ (exp x) -1)

simplify1.5s

Counts
48 → 58
Calls
48 calls:
Slowest
325.0ms
(/ (* (* (+ (exp x) -1) (+ (exp x) -1)) (+ (exp x) -1)) (* (* x x) x))
200.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
127.0ms
(* -1 (/ (- 1 (exp x)) x))
104.0ms
(+ (pow (exp x) 3) (pow -1 3))
81.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))

prune390.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes52.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.3b

bsearch50.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
981.0ms2233×body1280valid
500.0ms1702×body640valid
433.0ms5495×body80valid
173.0ms776×body320valid
54.0ms431×body160valid