Details

Time bar (total: 14.6s)

sample131.0ms

Algorithm
intervals
Results
90.0ms180×body1280valid
14.0ms266×body80valid
13.0ms41×body640valid
4.0ms20×body320valid
1.0ms9×body160valid

simplify80.0ms

Calls
1 calls:
Slowest
80.0ms
(+ (- (exp x) 2) (exp (- x)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.7b

localize24.0ms

Local error

Found 2 expressions with local error:

4.2b
(+ (- (exp x) 2) (exp (- x)))
0.0b
(- (exp x) 2)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
4×add-sqr-sqrt frac-add add-cube-cbrt add-log-exp
3×fma-def flip3-- fma-neg flip--
2×neg-sub0 exp-neg expm1-log1p-u pow1 associate-+l+ sub-neg add-cbrt-cube exp-diff add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative sum-log flip3-+ associate-+l- flip-+ distribute-lft-out
Calls
2 calls:
Slowest
37.0ms
(+ (- (exp x) 2) (exp (- x)))
10.0ms
(- (exp x) 2)

series101.0ms

Calls
2 calls:
Slowest
87.0ms
(+ (- (exp x) 2) (exp (- x)))
14.0ms
(- (exp x) 2)

simplify2.2s

Calls
23 calls:
Slowest
468.0ms
(+ (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) (exp 0)))
405.0ms
(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp 0)))
240.0ms
(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) 1))
198.0ms
(+ (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) 1))
140.0ms
(* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp x))

prune372.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (pow x 4) 1/12 (* x x))
0.0b
(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Calls
2 calls:
Slowest
0.0ms
(fma (pow x 4) 1/12 (* x x))
0.0ms
(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))

series80.0ms

Calls
2 calls:
Slowest
48.0ms
(fma (pow x 4) 1/12 (* x x))
32.0ms
(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))

simplify178.0ms

Calls
6 calls:
Slowest
51.0ms
(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
51.0ms
(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
38.0ms
(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
13.0ms
(+ (pow x 2) (* 1/12 (pow x 4)))
13.0ms
(+ (pow x 2) (* 1/12 (pow x 4)))

prune285.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.1b
(fma (+ -3 (* (exp x) (exp x))) (exp x) 2)
0.0b
(* (exp x) (exp x))
0.0b
(/ (fma (+ -3 (* (exp x) (exp x))) (exp x) 2) (* (+ (exp x) 2) (exp x)))
0.0b
(+ (exp x) 2)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube
9×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
8×add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-def times-frac associate-*r* associate-*l* associate-/l*
2×cbrt-undiv flip3-+ div-exp associate-*l/ prod-exp associate-/r/ cbrt-unprod flip-+
1×pow2 +-commutative clear-num associate-/r* frac-2neg pow-plus pow-prod-down *-commutative pow-prod-up fma-udef div-inv
Calls
4 calls:
Slowest
10.0ms
(/ (fma (+ -3 (* (exp x) (exp x))) (exp x) 2) (* (+ (exp x) 2) (exp x)))
4.0ms
(* (exp x) (exp x))
3.0ms
(+ (exp x) 2)
0.0ms
(fma (+ -3 (* (exp x) (exp x))) (exp x) 2)

series173.0ms

Calls
4 calls:
Slowest
112.0ms
(/ (fma (+ -3 (* (exp x) (exp x))) (exp x) 2) (* (+ (exp x) 2) (exp x)))
41.0ms
(fma (+ -3 (* (exp x) (exp x))) (exp x) 2)
12.0ms
(* (exp x) (exp x))
6.0ms
(+ (exp x) 2)

simplify2.7s

Calls
40 calls:
Slowest
349.0ms
(/ (- (+ (pow (exp x) 3) 2) (* 3 (exp x))) (* (exp x) (+ (exp x) 2)))
348.0ms
(/ (- (+ (pow (exp x) 3) 2) (* 3 (exp x))) (* (exp x) (+ (exp x) 2)))
258.0ms
(/ (* (* (fma (+ -3 (* (exp x) (exp x))) (exp x) 2) (fma (+ -3 (* (exp x) (exp x))) (exp x) 2)) (fma (+ -3 (* (exp x) (exp x))) (exp x) 2)) (* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x))))
253.0ms
(/ (* (* (fma (+ -3 (* (exp x) (exp x))) (exp x) 2) (fma (+ -3 (* (exp x) (exp x))) (exp x) 2)) (fma (+ -3 (* (exp x) (exp x))) (exp x) 2)) (* (* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x))) (* (+ (exp x) 2) (exp x))))
123.0ms
(+ (* 4 (pow x 3)) (+ (* 3 (pow x 2)) (* 13/4 (pow x 4))))

prune709.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.1b
(fma (+ -3 (* (exp x) (exp x))) (exp x) 2)
0.0b
(cbrt (+ (exp x) 2))
0.0b
(cbrt (+ (exp x) 2))
0.0b
(cbrt (+ (exp x) 2))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+
1×fma-udef
Calls
4 calls:
Slowest
3.0ms
(cbrt (+ (exp x) 2))
3.0ms
(cbrt (+ (exp x) 2))
3.0ms
(cbrt (+ (exp x) 2))
0.0ms
(fma (+ -3 (* (exp x) (exp x))) (exp x) 2)

series431.0ms

Calls
4 calls:
Slowest
134.0ms
(cbrt (+ (exp x) 2))
127.0ms
(cbrt (+ (exp x) 2))
120.0ms
(cbrt (+ (exp x) 2))
51.0ms
(fma (+ -3 (* (exp x) (exp x))) (exp x) 2)

simplify1.4s

Calls
27 calls:
Slowest
234.0ms
(+ (* 7/162 (* (pow x 2) (pow 3 1/3))) (+ (pow 3 1/3) (* 1/9 (* x (pow 3 1/3)))))
215.0ms
(+ (* 7/162 (* (pow x 2) (pow 3 1/3))) (+ (pow 3 1/3) (* 1/9 (* x (pow 3 1/3)))))
212.0ms
(+ (* 7/162 (* (pow x 2) (pow 3 1/3))) (+ (pow 3 1/3) (* 1/9 (* x (pow 3 1/3)))))
122.0ms
(+ (* 4 (pow x 3)) (+ (* 3 (pow x 2)) (* 13/4 (pow x 4))))
107.0ms
(- (+ (pow (exp x) 3) 2) (* 3 (exp x)))

prune719.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes19.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch1.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
3.3s5716×body1280valid
837.0ms7933×body80valid
398.0ms1210×body640valid
149.0ms616×body320valid
35.0ms278×body160valid