Details

Time bar (total: 19.4s)

sample99.0ms

Algorithm
intervals
Results
39.0ms105×body1280valid
19.0ms79×body640valid
13.0ms365×pre80true
8.0ms48×body320valid
5.0ms116×body80valid
2.0ms17×body160valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (exp x) 1)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.3b

localize25.0ms

Local error

Found 1 expressions with local error:

5.5b
(- (exp x) 1)

rewrite17.0ms

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
16.0ms
(- (exp x) 1)

series25.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
25.0ms
(- (exp x) 1)

simplify313.0ms

Counts
10 → 20
Calls
10 calls:
Slowest
181.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
29.0ms
(/ (exp (exp x)) (exp 1))
18.0ms
(- (sqrt (exp x)) (sqrt 1))
17.0ms
(+ (sqrt (exp x)) (sqrt 1))
16.0ms
(+ (sqrt (exp x)) 1)

prune158.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)

rewrite56.0ms

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
37.0ms
(* (* x x) (+ (* x 1/6) 1/2))
10.0ms
(* x 1/6)
7.0ms
(+ (* x 1/6) 1/2)

series184.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
119.0ms
(* (* x x) (+ (* x 1/6) 1/2))
43.0ms
(+ (* x 1/6) 1/2)
22.0ms
(* x 1/6)

simplify1.8s

Counts
34 → 64
Calls
34 calls:
Slowest
303.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
242.0ms
(+ (* (* x 1/6) (* x 1/6)) (- (* 1/2 1/2) (* (* x 1/6) 1/2)))
239.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
214.0ms
(+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))
148.0ms
(* (* (* x x) x) (* (* 1/6 1/6) 1/6))

prune421.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

5.5b
(- (* (exp x) (exp x)) (* 1 1))
0.0b
(* (exp x) (exp x))
0.0b
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
0.0b
(+ (exp x) 1)

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
26×add-sqr-sqrt
24×add-cube-cbrt
18×exp-prod
16×times-frac
11×pow1
8×add-cbrt-cube add-log-exp
6×add-exp-log distribute-lft-out difference-of-squares
4×associate-/r* pow-prod-down pow-sqr pow-prod-up insert-posit16 associate-/l*
3×swap-sqr associate-*r* associate-*l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×pow2 cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg pow-plus diff-log div-sub div-exp prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 104
Calls
4 calls:
Slowest
46.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
15.0ms
(- (* (exp x) (exp x)) (* 1 1))
13.0ms
(* (exp x) (exp x))
6.0ms
(+ (exp x) 1)

series100.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
46.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
26.0ms
(- (* (exp x) (exp x)) (* 1 1))
16.0ms
(* (exp x) (exp x))
13.0ms
(+ (exp x) 1)

simplify5.8s

Counts
101 → 116
Calls
101 calls:
Slowest
743.0ms
(/ (* (* (- (* (exp x) (exp x)) (* 1 1)) (- (* (exp x) (exp x)) (* 1 1))) (- (* (exp x) (exp x)) (* 1 1))) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
366.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
361.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
256.0ms
(- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (* 1 1) (* 1 1)))
252.0ms
(- (pow (* (exp x) (exp x)) 3) (pow (* 1 1) 3))

prune618.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

5.5b
(- (/ (* (exp x) (exp x)) (+ (exp x) 1)) (/ (* 1 1) (+ (exp x) 1)))
0.0b
(* (exp x) (exp x))
0.0b
(/ (* (exp x) (exp x)) (+ (exp x) 1))
0.0b
(/ (* 1 1) (+ (exp x) 1))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
28×add-sqr-sqrt
18×exp-prod add-cube-cbrt
17×add-exp-log
16×add-cbrt-cube
14×times-frac
11×pow1
8×associate-/r* associate-/r/
7×div-exp
6×prod-exp div-inv add-log-exp
5×distribute-rgt-out-- distribute-lft-out
4×cbrt-undiv flip3-+ 1-exp pow-prod-down pow-sqr pow-prod-up flip-+ insert-posit16 difference-of-squares
3×swap-sqr associate-*r* associate-*l* cbrt-unprod
2×clear-num frac-2neg associate-/l*
1×pow2 sub-neg pow-plus flip3-- diff-log *-commutative frac-sub flip-- distribute-lft-out-- sub-div unswap-sqr
Counts
4 → 115
Calls
4 calls:
Slowest
79.0ms
(- (/ (* (exp x) (exp x)) (+ (exp x) 1)) (/ (* 1 1) (+ (exp x) 1)))
23.0ms
(/ (* (exp x) (exp x)) (+ (exp x) 1))
18.0ms
(/ (* 1 1) (+ (exp x) 1))
12.0ms
(* (exp x) (exp x))

series165.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(- (/ (* (exp x) (exp x)) (+ (exp x) 1)) (/ (* 1 1) (+ (exp x) 1)))
38.0ms
(/ (* (exp x) (exp x)) (+ (exp x) 1))
25.0ms
(/ (* 1 1) (+ (exp x) 1))
21.0ms
(* (exp x) (exp x))

simplify5.3s

Counts
114 → 127
Calls
114 calls:
Slowest
508.0ms
(- (+ (* 1/48 (pow x 3)) 1/2) (* 1/4 x))
421.0ms
(/ (* (* (* 1 1) 1) (* (* 1 1) 1)) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
393.0ms
(/ (* (* (* 1 1) (* 1 1)) (* 1 1)) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
234.0ms
(- (* (* (exp x) (exp x)) (+ (exp x) 1)) (* (+ (exp x) 1) (* 1 1)))
219.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))

prune898.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.5s3438×body1280valid
475.0ms2494×body640valid
395.0ms11996×pre80true
190.0ms1255×body320valid
189.0ms4182×body80valid
50.0ms627×body160valid