Details

Time bar (total: 19.8s)

sample54.0ms

Algorithm
intervals
Results
24.0ms127×body1280valid
9.0ms76×body640valid
7.0ms388×pre80true
3.0ms140×body80valid
3.0ms34×body320valid
1.0ms11×body160valid

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(- (exp x) 1)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.4b

localize5.0ms

Local error

Found 1 expressions with local error:

4.0b
(- (exp x) 1)

rewrite16.0ms

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)

series39.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
39.0ms
(- (exp x) 1)

simplify403.0ms

Counts
10 → 20
Calls
10 calls:
Slowest
266.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
27.0ms
(/ (exp (exp x)) (exp 1))
17.0ms
(- (sqrt (exp x)) 1)
16.0ms
(- (exp x) 1)
16.0ms
(- (exp x) 1)

prune195.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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
38.0ms
(* (* x x) (+ (* x 1/6) 1/2))
10.0ms
(* x 1/6)

series114.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
87.0ms
(* (* x x) (+ (* x 1/6) 1/2))
27.0ms
(* x 1/6)

simplify1.8s

Counts
30 → 49
Calls
30 calls:
Slowest
320.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
263.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
237.0ms
(+ (* (* x 1/6) (* x 1/6)) (- (* 1/2 1/2) (* (* x 1/6) 1/2)))
174.0ms
(+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))
168.0ms
(+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))

prune343.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b
(- (* (exp x) (exp x)) (* 1 1))
0.0b
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
0.0b
(* (exp x) (exp x))
0.0b
(+ (exp x) 1)

rewrite92.0ms

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
52.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
14.0ms
(- (* (exp x) (exp x)) (* 1 1))
13.0ms
(* (exp x) (exp x))
11.0ms
(+ (exp x) 1)

series120.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
36.0ms
(- (* (exp x) (exp x)) (* 1 1))
13.0ms
(* (exp x) (exp x))
11.0ms
(+ (exp x) 1)

simplify5.8s

Counts
101 → 116
Calls
101 calls:
Slowest
710.0ms
(/ (* (* (- (* (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)))
409.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
320.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
262.0ms
(/ (exp (* (exp x) (exp x))) (exp (* 1 1)))
255.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))

prune756.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

3.9b
(+ -1 (* (exp x) (exp x)))
0.1b
(exp (- (log (+ -1 (* (exp x) (exp x)))) (log (+ (exp x) 1))))
0.0b
(* (exp x) (exp x))
0.0b
(- (log (+ -1 (* (exp x) (exp x)))) (log (+ (exp x) 1)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
26×exp-prod
24×add-sqr-sqrt
19×pow1
18×add-cube-cbrt
10×log-prod
8×log-pow distribute-lft-out--
7×exp-sum add-log-exp
6×log-div add-cbrt-cube associate--l+
4×flip3-+ pow-prod-down add-exp-log pow-sqr pow-prod-up flip-+ insert-posit16 associate--r+ associate--r-
3×swap-sqr associate-*r* associate-*l*
2×associate--l- sub-neg diff-log difference-of-squares rem-exp-log
1×pow2 +-commutative sum-log pow-plus flip3-- exp-diff prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out unswap-sqr
Counts
4 → 102
Calls
4 calls:
Slowest
31.0ms
(exp (- (log (+ -1 (* (exp x) (exp x)))) (log (+ (exp x) 1))))
18.0ms
(* (exp x) (exp x))
12.0ms
(- (log (+ -1 (* (exp x) (exp x)))) (log (+ (exp x) 1)))
5.0ms
(+ -1 (* (exp x) (exp x)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(- (log (+ -1 (* (exp x) (exp x)))) (log (+ (exp x) 1)))
195.0ms
(exp (- (log (+ -1 (* (exp x) (exp x)))) (log (+ (exp x) 1))))
32.0ms
(+ -1 (* (exp x) (exp x)))
23.0ms
(* (exp x) (exp x))

simplify5.4s

Counts
87 → 114
Calls
87 calls:
Slowest
370.0ms
(exp (- (log (+ -1 (* (exp x) (exp x)))) (log (+ (pow (exp x) 3) (pow 1 3)))))
364.0ms
(log (+ (pow -1 3) (pow (* (exp x) (exp x)) 3)))
333.0ms
(- (log (- (pow (exp x) 2) 1)) (log (+ (exp x) 1)))
303.0ms
(- (log (- (pow (exp x) 2) 1)) (log (+ (exp x) 1)))
260.0ms
(+ (* 2 x) (+ (* 4/3 (pow x 3)) (* 2 (pow x 2))))

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes106.0ms

Accuracy

98.9% (0.0b remaining)

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

bsearch34.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s3491×body1280valid
579.0ms1313×body320valid
436.0ms2439×body640valid
389.0ms11990×pre80true
124.0ms4165×body80valid
45.0ms582×body160valid