Details

Time bar (total: 7.4s)

sample46.0ms

Algorithm
intervals
Results
17.0ms64×body1280valid
11.0ms58×body640valid
6.0ms162×body80valid
4.0ms27×body320valid
2.0ms18×body160valid

simplify25.0ms

Calls
1 calls:
Slowest
25.0ms
(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize8.0ms

Local error

Found 2 expressions with local error:

4.8b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×associate-/l*
3×*-un-lft-identity add-cube-cbrt
2×pow1 flip3-- add-cbrt-cube difference-of-sqr-1 add-exp-log insert-posit16 flip-- add-log-exp associate-/l/
1×clear-num sub-neg frac-2neg div-sub div-inv
Calls
2 calls:
Slowest
8.0ms
(/ (- (exp x) 1) x)
3.0ms
(- (exp x) 1)

series33.0ms

Calls
2 calls:
Slowest
22.0ms
(/ (- (exp x) 1) x)
11.0ms
(- (exp x) 1)

simplify346.0ms

Calls
13 calls:
Slowest
101.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
82.0ms
(* -1 (/ (- 1 (exp x)) x))
43.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
27.0ms
(- (* (exp x) (exp x)) (* 1 1))
19.0ms
(- (pow (exp x) 3) (pow 1 3))

prune198.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b
(* 1/6 x)
0.0b
(* x (+ (* 1/6 x) 1/2))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
2×pow1 add-cbrt-cube associate-*r/ add-exp-log *-commutative insert-posit16 add-log-exp
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+
Calls
2 calls:
Slowest
3.0ms
(* x (+ (* 1/6 x) 1/2))
0.0ms
(* 1/6 x)

series31.0ms

Calls
2 calls:
Slowest
24.0ms
(* x (+ (* 1/6 x) 1/2))
7.0ms
(* 1/6 x)

simplify290.0ms

Calls
13 calls:
Slowest
165.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
30.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
28.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
28.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
9.0ms
(- (* 1/6 x) 1/2)

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

4.0b
(- (/ (exp x) x) (/ 1 x))
0.0b
(/ (exp x) x)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
5×add-sqr-sqrt div-inv
4×add-log-exp
3×add-cube-cbrt associate-/l*
2×pow1 add-cbrt-cube distribute-rgt-out-- add-exp-log insert-posit16 distribute-lft-out--
1×clear-num sub-neg frac-2neg flip3-- diff-log frac-sub flip-- sub-div difference-of-squares
Calls
2 calls:
Slowest
6.0ms
(- (/ (exp x) x) (/ 1 x))
3.0ms
(/ (exp x) x)

series32.0ms

Calls
2 calls:
Slowest
18.0ms
(- (/ (exp x) x) (/ 1 x))
13.0ms
(/ (exp x) x)

simplify305.0ms

Calls
20 calls:
Slowest
82.0ms
(* -1 (/ (- 1 (exp x)) x))
43.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
36.0ms
(/ (exp (/ (exp x) x)) (exp (/ 1 x)))
20.0ms
(+ (* 1/2 x) (+ (/ 1 x) 1))
17.0ms
(- (/ (exp x) x) (/ 1 x))

prune191.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b
(- (exp (+ (+ x x) x)) 1)
0.0b
(/ (- (exp (+ (+ x x) x)) 1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
0.0b
(* (exp x) (exp x))
0.0b
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×pow1 add-log-exp
8×*-un-lft-identity add-cbrt-cube add-cube-cbrt
6×add-exp-log
4×times-frac insert-posit16 associate-/l*
3×sum-log difference-of-sqr-1 associate-*r* associate-*l*
2×flip3-+ flip3-- associate-*r/ associate-/r/ flip-+ flip-- associate-/l/
1×pow2 cbrt-undiv +-commutative associate-+r+ clear-num associate-/r* sub-neg frac-2neg pow-plus div-sub div-exp pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod div-inv
Calls
4 calls:
Slowest
59.0ms
(/ (- (exp (+ (+ x x) x)) 1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
23.0ms
(- (exp (+ (+ x x) x)) 1)
10.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
4.0ms
(* (exp x) (exp x))

series99.0ms

Calls
4 calls:
Slowest
58.0ms
(/ (- (exp (+ (+ x x) x)) 1) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
17.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
15.0ms
(- (exp (+ (+ x x) x)) 1)
9.0ms
(* (exp x) (exp x))

simplify2.8s

Calls
46 calls:
Slowest
377.0ms
(/ (* (* (- (exp (+ (+ x x) x)) 1) (- (exp (+ (+ x x) x)) 1)) (- (exp (+ (+ x x) x)) 1)) (* (* (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
309.0ms
(/ (exp (+ (+ x x) x)) (* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
208.0ms
(+ (* (* (exp x) (exp x)) (* (exp x) (exp x))) (- (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))) (* (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
161.0ms
(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))
160.0ms
(/ (- (exp (* 3 x)) 1) (* (+ (pow (exp x) 2) (+ (exp x) 1)) x))

prune582.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch66.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
959.0ms2269×body1280valid
382.0ms1619×body640valid
260.0ms5458×body80valid
138.0ms844×body320valid
60.0ms437×body160valid