Details

Time bar (total: 1.8m)

sample78.0ms

Algorithm
intervals
Results
36.0ms119×body1280valid
12.0ms67×body640valid
10.0ms375×pre80true
4.0ms38×body320valid
4.0ms129×body80valid
2.0ms22×body160valid

simplify18.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.9b

localize6.0ms

Local error

Found 1 expressions with local error:

7.1b
(- (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)

series15.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
15.0ms
(- (exp x) 1)

simplify930.0ms

Counts
25 → 20
Calls
25 calls:
Slowest
253.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
154.0ms
(* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1))
84.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
61.0ms
(- (pow (exp x) 3) (pow 1 3))
56.0ms
(- (* (exp x) (exp x)) (* 1 1))

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×associate-*r*
5×*-un-lft-identity add-cube-cbrt
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ *-commutative insert-posit16 add-log-exp unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+
Counts
2 → 43
Calls
2 calls:
Slowest
46.0ms
(* (* x x) (+ (* x 1/6) 1/2))
11.0ms
(* x 1/6)

series94.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
77.0ms
(* (* x x) (+ (* x 1/6) 1/2))
17.0ms
(* x 1/6)

simplify3.6s

Counts
51 → 49
Calls
51 calls:
Slowest
389.0ms
(* (* x x) (+ (pow (* x 1/6) 3) (pow 1/2 3)))
278.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
267.0ms
(* (* (* (* x x) (+ (* x 1/6) 1/2)) (* (* x x) (+ (* x 1/6) 1/2))) (* (* x x) (+ (* x 1/6) 1/2)))
262.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
208.0ms
(+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))

prune371.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

7.2b
(+ (exp (+ x (+ x x))) -1)
0.0b
(/ (+ (exp (+ x (+ x x))) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
0.0b
(* (exp x) (+ 1 (exp x)))
0.0b
(+ (* (exp x) (+ 1 (exp x))) 1)

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
23×add-sqr-sqrt
16×add-cube-cbrt
15×times-frac
8×add-cbrt-cube add-log-exp
7×add-exp-log
6×pow1 distribute-lft-out
5×difference-of-sqr--1 flip3-+ flip-+ associate-/l*
4×associate-*r* insert-posit16
3×associate-/r* associate-*l*
2×distribute-rgt-in +-commutative associate-+l+ sum-log distribute-lft-in associate-*r/ associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 92
Calls
4 calls:
Slowest
332.0ms
(/ (+ (exp (+ x (+ x x))) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
113.0ms
(+ (exp (+ x (+ x x))) -1)
32.0ms
(* (exp x) (+ 1 (exp x)))
12.0ms
(+ (* (exp x) (+ 1 (exp x))) 1)

series169.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(/ (+ (exp (+ x (+ x x))) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
43.0ms
(+ (* (exp x) (+ 1 (exp x))) 1)
32.0ms
(* (exp x) (+ 1 (exp x)))
20.0ms
(+ (exp (+ x (+ x x))) -1)

simplify15.9s

Counts
125 → 104
Calls
125 calls:
Slowest
684.0ms
(* (+ (* (exp x) (+ 1 (exp x))) 1) (+ (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (- (* -1 -1) (* (exp (+ x (+ x x))) -1))))
672.0ms
(* (+ (* (exp x) (+ 1 (exp x))) 1) (- (exp (+ x (+ x x))) -1))
660.0ms
(* (* (+ (* (exp x) (+ 1 (exp x))) 1) (+ (* (exp x) (+ 1 (exp x))) 1)) (+ (* (exp x) (+ 1 (exp x))) 1))
504.0ms
(* (* (* (exp x) (exp x)) (exp x)) (* (* (+ 1 (exp x)) (+ 1 (exp x))) (+ 1 (exp x))))
438.0ms
(/ (+ (exp (+ x (+ x x))) -1) (- (* (* (exp x) (+ 1 (exp x))) (* (exp x) (+ 1 (exp x)))) (* 1 1)))

prune613.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

7.1b
(- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))
0.0b
(* (exp (+ x (+ x x))) (exp (+ x (+ x x))))
0.0b
(- (exp (+ x (+ x x))) -1)
0.0b
(/ (/ (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (exp (+ x (+ x x))) -1)) (+ (* (exp x) (+ 1 (exp x))) 1))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
289×*-un-lft-identity
189×add-sqr-sqrt
158×times-frac
144×exp-prod
102×distribute-lft-out
99×add-cube-cbrt
48×distribute-rgt1-in
38×difference-of-squares
36×distribute-rgt-out
26×associate-/l*
25×pow-prod-down pow-sqr pow-prod-up
24×distribute-lft1-in
17×distribute-lft-out--
11×pow1 add-cbrt-cube
10×associate-/r/
9×add-exp-log
8×add-log-exp
6×flip3-- flip--
5×div-inv
4×swap-sqr associate-*r* associate-*l* exp-sum insert-posit16
3×cbrt-undiv associate-/r* div-exp
2×sub-neg diff-log div-sub
1×pow2 clear-num frac-2neg flip3-+ pow-plus prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr associate-/l/
Counts
4 → 256
Calls
4 calls:
Slowest
1.0s
(/ (/ (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (exp (+ x (+ x x))) -1)) (+ (* (exp x) (+ 1 (exp x))) 1))
348.0ms
(* (exp (+ x (+ x x))) (exp (+ x (+ x x))))
333.0ms
(- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))
160.0ms
(- (exp (+ x (+ x x))) -1)

series261.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(/ (/ (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (exp (+ x (+ x x))) -1)) (+ (* (exp x) (+ 1 (exp x))) 1))
53.0ms
(- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))
29.0ms
(* (exp (+ x (+ x x))) (exp (+ x (+ x x))))
20.0ms
(- (exp (+ x (+ x x))) -1)

simplify1.3m

Counts
357 → 268
Calls
357 calls:
Slowest
722.0ms
(/ (/ (* (* (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))) (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))) (* (* (- (exp (+ x (+ x x))) -1) (- (exp (+ x (+ x x))) -1)) (- (exp (+ x (+ x x))) -1))) (* (* (+ (* (exp x) (+ 1 (exp x))) 1) (+ (* (exp x) (+ 1 (exp x))) 1)) (+ (* (exp x) (+ 1 (exp x))) 1)))
659.0ms
(/ (/ (cbrt (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))) (- (exp (+ x (+ x x))) -1)) (+ (* (exp x) (+ 1 (exp x))) 1))
630.0ms
(/ (* (cbrt (/ (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (exp (+ x (+ x x))) -1))) (cbrt (/ (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1)) (- (exp (+ x (+ x x))) -1)))) (sqrt (+ (* (exp x) (+ 1 (exp x))) 1)))
630.0ms
(/ (/ (- (exp (+ x (+ x x))) -1) (- (sqrt (exp (+ x (+ x x)))) (sqrt -1))) (+ (* (exp x) (+ 1 (exp x))) 1))
600.0ms
(/ (/ (sqrt (- (* (exp (+ x (+ x x))) (exp (+ x (+ x x)))) (* -1 -1))) (* (cbrt (- (exp (+ x (+ x x))) -1)) (cbrt (- (exp (+ x (+ x x))) -1)))) 1)

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes92.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch3.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.6s3486×body1280valid
583.0ms2422×body640valid
365.0ms11970×pre80true
199.0ms1279×body320valid
134.0ms4180×body80valid
48.0ms603×body160valid