Details

Time bar (total: 25.2s)

sample47.0ms

Algorithm
intervals
Results
17.0ms64×body1280valid
9.0ms51×body640valid
7.0ms184×body80valid
6.0ms31×body320valid
1.0ms10×body160valid

simplify31.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
31.0ms
(/ (- (exp x) 1) x)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite68.0ms

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
49.0ms
(/ (- (exp x) 1) x)
17.0ms
(- (exp x) 1)

series71.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
52.0ms
(/ (- (exp x) 1) x)
19.0ms
(- (exp x) 1)

simplify2.0s

Counts
67 → 70
Calls
67 calls:
Slowest
234.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
185.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
172.0ms
(* -1 (/ (- 1 (exp x)) x))
67.0ms
(- (pow (exp x) 3) (pow 1 3))
60.0ms
(/ (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))) (* (cbrt x) (cbrt x)))

prune618.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)

rewrite40.0ms

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
Counts
3 → 54
Calls
3 calls:
Slowest
20.0ms
(* x (+ (* 1/6 x) 1/2))
11.0ms
(* 1/6 x)
8.0ms
(+ (* 1/6 x) 1/2)

series167.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
90.0ms
(* x (+ (* 1/6 x) 1/2))
61.0ms
(+ (* 1/6 x) 1/2)
16.0ms
(* 1/6 x)

simplify1.1s

Counts
33 → 63
Calls
33 calls:
Slowest
259.0ms
(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
224.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
213.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
72.0ms
(* (exp (* 1/6 x)) (exp 1/2))
54.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune542.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite591.0ms

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
396.0ms
(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
122.0ms
(+ (exp (+ x (+ x x))) -1)
43.0ms
(exp (+ x (+ x x)))
27.0ms
(* (exp x) (exp x))

series161.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ (+ (exp (+ x (+ x x))) -1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
31.0ms
(+ (exp (+ x (+ x x))) -1)
21.0ms
(* (exp x) (exp x))
9.0ms
(exp (+ x (+ x x)))

simplify7.1s

Counts
91 → 115
Calls
91 calls:
Slowest
910.0ms
(/ (* (* (+ (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))))))
732.0ms
(/ (* (* (+ (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))))))
720.0ms
(+ (* (* (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)))))
386.0ms
(+ (pow (exp (+ x (+ x x))) 3) (pow -1 3))
380.0ms
(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite665.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
30×add-sqr-sqrt
20×add-cube-cbrt
15×times-frac
14×distribute-lft-out
12×exp-prod add-log-exp
8×add-cbrt-cube
7×add-exp-log
6×pow1
5×difference-of-sqr--1 associate-/l*
4×sum-log distribute-lft1-in flip3-+ associate-*r* flip-+ insert-posit16
3×associate-/r* distribute-rgt-out associate-*l* rem-exp-log
2×distribute-rgt1-in associate-*r/ associate-/r/ associate-/l/
1×distribute-rgt-in cbrt-undiv +-commutative clear-num frac-2neg distribute-lft-in div-exp exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 102
Calls
4 calls:
Slowest
410.0ms
(/ (+ (exp (+ (+ x x) x)) -1) (+ (* (exp x) (+ (exp x) 1)) 1))
115.0ms
(+ (exp (+ (+ x x) x)) -1)
87.0ms
(exp (+ (+ x x) x))
50.0ms
(* (exp x) (+ (exp x) 1))

series144.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(/ (+ (exp (+ (+ x x) x)) -1) (+ (* (exp x) (+ (exp x) 1)) 1))
33.0ms
(+ (exp (+ (+ x x) x)) -1)
21.0ms
(* (exp x) (+ (exp x) 1))
9.0ms
(exp (+ (+ x x) x))

simplify7.0s

Counts
88 → 114
Calls
88 calls:
Slowest
451.0ms
(+ (pow (exp (+ (+ x x) x)) 3) (pow -1 3))
357.0ms
(* (* (* (exp x) (exp x)) (exp x)) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
287.0ms
(+ (* 3 x) (+ (* 9/2 (pow x 3)) (* 9/2 (pow x 2))))
276.0ms
(+ (* (* (exp x) (+ (exp x) 1)) (* (exp x) (+ (exp x) 1))) (- (* 1 1) (* (* (exp x) (+ (exp x) 1)) 1)))
268.0ms
(- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* -1 -1))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

98.4% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.4b

bsearch85.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
999.0ms2259×body1280valid
586.0ms1636×body640valid
385.0ms5475×body80valid
189.0ms808×body320valid
55.0ms430×body160valid