Details

Time bar (total: 24.4s)

sample76.0ms

Algorithm
intervals
Results
29.0ms97×body1280valid
16.0ms87×body640valid
10.0ms382×pre80true
5.0ms45×body320valid
4.0ms132×body80valid
2.0ms21×body160valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (exp x) 1)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.3b

localize10.0ms

Local error

Found 1 expressions with local error:

5.9b
(- (exp x) 1)

rewrite14.0ms

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
14.0ms
(- (exp x) 1)

series15.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
14.0ms
(- (exp x) 1)

simplify366.0ms

Counts
10 → 20
Calls
10 calls:
Slowest
203.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
28.0ms
(/ (exp (exp x)) (exp 1))
21.0ms
(- (sqrt (exp x)) (sqrt 1))
19.0ms
(- (exp x) 1)
19.0ms
(+ (sqrt (exp x)) (sqrt 1))

prune160.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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 1/6) 1/2)

rewrite39.0ms

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×flip3-+ associate-*r/ *-commutative flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
3 → 55
Calls
3 calls:
Slowest
26.0ms
(* (* x x) (+ (* x 1/6) 1/2))
7.0ms
(+ (* x 1/6) 1/2)
5.0ms
(* x 1/6)

series165.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
84.0ms
(* (* x x) (+ (* x 1/6) 1/2))
61.0ms
(+ (* x 1/6) 1/2)
19.0ms
(* x 1/6)

simplify2.1s

Counts
34 → 64
Calls
34 calls:
Slowest
329.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
304.0ms
(+ (* (* x 1/6) (* x 1/6)) (- (* 1/2 1/2) (* (* x 1/6) 1/2)))
280.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
195.0ms
(+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))
190.0ms
(+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))

prune471.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

5.8b
(- (sqrt (exp x)) 1)
0.0b
(* (+ (sqrt (exp x)) 1) (- (sqrt (exp x)) 1))
0.0b
(+ (sqrt (exp x)) 1)
0.0b
(sqrt (exp x))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
24×*-un-lft-identity
13×sqrt-prod
11×associate-*r*
8×add-cube-cbrt add-log-exp difference-of-squares
7×pow1
6×add-cbrt-cube add-exp-log
5×associate-*l*
4×frac-times sqrt-pow1 flip3-+ flip3-- difference-of-sqr-1 flip-+ insert-posit16 flip-- distribute-lft-out distribute-lft-out--
3×exp-prod sub-neg
2×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/
1×+-commutative rem-sqrt-square sum-log pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 93
Calls
4 calls:
Slowest
63.0ms
(* (+ (sqrt (exp x)) 1) (- (sqrt (exp x)) 1))
10.0ms
(- (sqrt (exp x)) 1)
8.0ms
(+ (sqrt (exp x)) 1)
2.0ms
(sqrt (exp x))

series146.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(* (+ (sqrt (exp x)) 1) (- (sqrt (exp x)) 1))
35.0ms
(- (sqrt (exp x)) 1)
28.0ms
(+ (sqrt (exp x)) 1)
13.0ms
(sqrt (exp x))

simplify5.9s

Counts
73 → 105
Calls
73 calls:
Slowest
549.0ms
(* (+ (pow (sqrt (exp x)) 3) (pow 1 3)) (- (pow (sqrt (exp x)) 3) (pow 1 3)))
478.0ms
(* (+ (pow (sqrt (exp x)) 3) (pow 1 3)) (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)))
436.0ms
(* (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)) (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)))
424.0ms
(* (+ (* (sqrt (exp x)) (sqrt (exp x))) (- (* 1 1) (* (sqrt (exp x)) 1))) (+ (* (sqrt (exp x)) (sqrt (exp x))) (+ (* 1 1) (* (sqrt (exp x)) 1))))
422.0ms
(* (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)) (- (sqrt (exp x)) 1))

prune721.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/48 x)
0.0b
(* (+ (sqrt (exp x)) 1) (* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x))
0.0b
(* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x)
0.0b
(* (+ (* 1/48 x) 1/8) x)

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×pow1 add-cbrt-cube add-exp-log
14×*-un-lft-identity associate-*l*
12×associate-*l/
11×add-cube-cbrt
10×associate-*r*
8×flip3-+ flip-+
6×pow-prod-down prod-exp cbrt-unprod
4×frac-times *-commutative insert-posit16 add-log-exp
3×unswap-sqr
2×associate-*r/ distribute-lft-out
1×sqrt-prod
Counts
4 → 90
Calls
4 calls:
Slowest
107.0ms
(* (+ (sqrt (exp x)) 1) (* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x))
57.0ms
(* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x)
19.0ms
(* (+ (* 1/48 x) 1/8) x)
5.0ms
(* 1/48 x)

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(* (+ (* 1/48 x) 1/8) x)
63.0ms
(* (+ (sqrt (exp x)) 1) (* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x))
34.0ms
(* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x)
27.0ms
(* 1/48 x)

simplify9.5s

Counts
64 → 102
Calls
64 calls:
Slowest
592.0ms
(* (+ (pow (* (+ (* 1/48 x) 1/8) x) 3) (pow 1/2 3)) x)
506.0ms
(* (- (* (* (+ (* 1/48 x) 1/8) x) (* (+ (* 1/48 x) 1/8) x)) (* 1/2 1/2)) x)
506.0ms
(+ (* (* (+ (* 1/48 x) 1/8) x) (* (+ (* 1/48 x) 1/8) x)) (- (* 1/2 1/2) (* (* (+ (* 1/48 x) 1/8) x) 1/2)))
496.0ms
(* (* (* (+ (sqrt (exp x)) 1) (+ (sqrt (exp x)) 1)) (+ (sqrt (exp x)) 1)) (* (* (* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) (+ (* (+ (* 1/48 x) 1/8) x) 1/2)) (+ (* (+ (* 1/48 x) 1/8) x) 1/2)) (* (* x x) x)))
415.0ms
(* (+ (pow (sqrt (exp x)) 3) (pow 1 3)) (* (+ (* (+ (* 1/48 x) 1/8) x) 1/2) x))

prune975.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes132.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s3407×body1280valid
556.0ms2471×body640valid
540.0ms4054×body80valid
465.0ms11859×pre80true
171.0ms1314×body320valid
78.0ms613×body160valid