Details

Time bar (total: 34.4s)

sample82.0ms

Algorithm
intervals
Results
27.0ms97×body1280valid
18.0ms93×body640valid
13.0ms415×pre80true
6.0ms168×body80valid
5.0ms43×body320valid
1.0ms14×body160valid

simplify24.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
24.0ms
(- (exp x) 1)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.2b

localize6.0ms

Local error

Found 1 expressions with local error:

4.4b
(- (exp x) 1)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×*-un-lft-identity
3×add-log-exp
2×difference-of-squares
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log difference-of-sqr-1 add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out--
Counts
1 → 17
Calls
1 calls:
Slowest
9.0ms
(- (exp x) 1)

series18.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
18.0ms
(- (exp x) 1)

simplify919.0ms

Counts
25 → 20
Calls
25 calls:
Slowest
244.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
154.0ms
(* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1))
83.0ms
(- (pow (exp x) 3) (pow 1 3))
71.0ms
(cbrt (- (exp x) 1))
50.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
6×*-un-lft-identity associate-*r* add-cube-cbrt
5×add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×insert-posit16
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ *-commutative flip-+ unswap-sqr
1×+-commutative sum-log
Counts
3 → 57
Calls
3 calls:
Slowest
54.0ms
(* (* x x) (+ (* x 1/6) 1/2))
13.0ms
(+ x (* (* x x) (+ (* x 1/6) 1/2)))
5.0ms
(* x 1/6)

series119.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
76.0ms
(* (* x x) (+ (* x 1/6) 1/2))
28.0ms
(+ x (* (* x x) (+ (* x 1/6) 1/2)))
15.0ms
(* x 1/6)

simplify7.4s

Counts
69 → 66
Calls
69 calls:
Slowest
388.0ms
(* (* x x) (+ (pow (* x 1/6) 3) (pow 1/2 3)))
370.0ms
(* (exp x) (exp (* (* x x) (+ (* x 1/6) 1/2))))
303.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
296.0ms
(exp (+ x (* (* x x) (+ (* x 1/6) 1/2))))
286.0ms
(+ (* x x) (- (* (* (* x x) (+ (* x 1/6) 1/2)) (* (* x x) (+ (* x 1/6) 1/2))) (* x (* (* x x) (+ (* x 1/6) 1/2)))))

prune527.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

4.4b
(- (sqrt (exp x)) 1)
0.0b
(* (+ (sqrt (exp x)) 1) (- (sqrt (exp x)) 1))
0.0b
(+ (sqrt (exp x)) 1)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
11×associate-*r*
10×sqrt-prod
8×difference-of-squares
7×add-log-exp
5×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
4×frac-times flip3-+ flip3-- difference-of-sqr-1 flip-+ flip-- distribute-lft-out distribute-lft-out--
3×sub-neg insert-posit16
2×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/
1×+-commutative sum-log diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 76
Calls
3 calls:
Slowest
83.0ms
(* (+ (sqrt (exp x)) 1) (- (sqrt (exp x)) 1))
10.0ms
(- (sqrt (exp x)) 1)
8.0ms
(+ (sqrt (exp x)) 1)

series117.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
67.0ms
(* (+ (sqrt (exp x)) 1) (- (sqrt (exp x)) 1))
33.0ms
(- (sqrt (exp x)) 1)
17.0ms
(+ (sqrt (exp x)) 1)

simplify11.9s

Counts
102 → 85
Calls
102 calls:
Slowest
655.0ms
(* (+ (sqrt (exp x)) 1) (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)))
601.0ms
(* (+ (pow (sqrt (exp x)) 3) (pow 1 3)) (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)))
560.0ms
(* (+ (pow (sqrt (exp x)) 3) (pow 1 3)) (- (pow (sqrt (exp x)) 3) (pow 1 3)))
536.0ms
(* (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)) (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)))
505.0ms
(* (+ (* (sqrt (exp x)) (sqrt (exp x))) (- (* 1 1) (* (sqrt (exp x)) 1))) (+ (* (sqrt (exp x)) (sqrt (exp x))) (+ (* 1 1) (* (sqrt (exp x)) 1))))

prune534.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

4.3b
(+ -1 (* (exp x) (exp x)))
0.3b
(/ (+ -1 (* (exp x) (exp x))) (+ (exp x) 1))
0.0b
(* (exp x) (exp x))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
24×add-sqr-sqrt
22×add-cube-cbrt
18×exp-prod
12×times-frac
10×pow1
7×add-cbrt-cube
5×add-exp-log add-log-exp
4×associate-/r* pow-prod-down pow-sqr pow-prod-up distribute-lft-out
3×flip3-+ swap-sqr associate-*r* associate-*l* flip-+ insert-posit16 associate-/l*
2×associate-/r/ associate-/l/
1×pow2 cbrt-undiv +-commutative clear-num sum-log frac-2neg pow-plus div-exp prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
3 → 83
Calls
3 calls:
Slowest
37.0ms
(/ (+ -1 (* (exp x) (exp x))) (+ (exp x) 1))
25.0ms
(* (exp x) (exp x))
7.0ms
(+ -1 (* (exp x) (exp x)))

series99.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
58.0ms
(/ (+ -1 (* (exp x) (exp x))) (+ (exp x) 1))
26.0ms
(+ -1 (* (exp x) (exp x)))
14.0ms
(* (exp x) (exp x))

simplify8.6s

Counts
108 → 92
Calls
108 calls:
Slowest
515.0ms
(+ (* -1 -1) (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* -1 (* (exp x) (exp x)))))
468.0ms
(* (+ (exp x) 1) (+ (* -1 -1) (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* -1 (* (exp x) (exp x))))))
353.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
348.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
322.0ms
(+ (pow -1 3) (pow (* (exp x) (exp x)) 3))

prune627.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes62.0ms

Accuracy

97.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.5b

bsearch46.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s3309×body1280valid
887.0ms2559×body640valid
345.0ms12090×pre80true
189.0ms4282×body80valid
156.0ms1312×body320valid
47.0ms628×body160valid