Details

Time bar (total: 13.3s)

sample152.0ms

Algorithm
intervals
Results
75.0ms105×body1280valid
33.0ms82×body640valid
20.0ms270×body80valid
9.0ms36×body320valid
4.0ms23×body160valid

simplify61.0ms

Calls
1 calls:
Slowest
61.0ms
(/ (- (exp x) (exp (- x))) 2)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.9b

localize32.0ms

Local error

Found 1 expressions with local error:

5.9b
(- (exp x) (exp (- x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×prod-diff
8×add-cube-cbrt
3×fma-neg add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Calls
1 calls:
Slowest
10.0ms
(- (exp x) (exp (- x)))

series43.0ms

Calls
1 calls:
Slowest
43.0ms
(- (exp x) (exp (- x)))

simplify1.0s

Calls
27 calls:
Slowest
88.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
78.0ms
(fma 1 (exp x) (- (* (exp (- x)) 1)))
63.0ms
(fma 1 (exp x) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
54.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
51.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (exp (- x)) 1)))

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (fma 1/3 (* x x) 2) x)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*l*
2×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
1×expm1-log1p-u pow1 add-cbrt-cube add-exp-log *-commutative insert-posit16 log1p-expm1-u add-log-exp
Calls
1 calls:
Slowest
3.0ms
(* (fma 1/3 (* x x) 2) x)

series33.0ms

Calls
1 calls:
Slowest
33.0ms
(* (fma 1/3 (* x x) 2) x)

simplify562.0ms

Calls
5 calls:
Slowest
400.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))
68.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))
63.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))
16.0ms
(* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2)))
14.0ms
(sqrt (fma 1/3 (* x x) 2))

prune177.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (fma 1/3 (* x x) 2))
1.0b
(cbrt (fma 1/3 (* x x) 2))
1.0b
(cbrt (fma 1/3 (* x x) 2))
0.5b
(* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (* (cbrt (fma 1/3 (* x x) 2)) x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod pow1 add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
1×associate-*r* associate-*l* *-commutative
Calls
4 calls:
Slowest
24.0ms
(* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (* (cbrt (fma 1/3 (* x x) 2)) x))
1.0ms
(cbrt (fma 1/3 (* x x) 2))
1.0ms
(cbrt (fma 1/3 (* x x) 2))
1.0ms
(cbrt (fma 1/3 (* x x) 2))

series315.0ms

Calls
4 calls:
Slowest
100.0ms
(cbrt (fma 1/3 (* x x) 2))
92.0ms
(cbrt (fma 1/3 (* x x) 2))
91.0ms
(cbrt (fma 1/3 (* x x) 2))
32.0ms
(* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (* (cbrt (fma 1/3 (* x x) 2)) x))

simplify3.7s

Calls
28 calls:
Slowest
440.0ms
(* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (* (* (* (cbrt (fma 1/3 (* x x) 2)) x) (* (cbrt (fma 1/3 (* x x) 2)) x)) (* (cbrt (fma 1/3 (* x x) 2)) x)))
373.0ms
(* (* (* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2)))) (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2)))) (* (* (* (cbrt (fma 1/3 (* x x) 2)) x) (* (cbrt (fma 1/3 (* x x) 2)) x)) (* (cbrt (fma 1/3 (* x x) 2)) x)))
341.0ms
(- (+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (pow 2 1/3)) (* 1/324 (* (pow x 4) (pow 2 1/3))))
339.0ms
(- (+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (pow 2 1/3)) (* 1/324 (* (pow x 4) (pow 2 1/3))))
316.0ms
(- (+ (* 2 (/ (exp (* 1/3 (- (log 1/3) (* 2 (log (/ 1 x)))))) (pow x 2))) (exp (* 1/3 (- (log 1/3) (* 2 (log (/ 1 x))))))) (* 4 (/ (exp (* 1/3 (- (log 1/3) (* 2 (log (/ 1 x)))))) (pow x 4))))

prune834.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

6.0b
(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x))))
0.0b
(sqrt (exp x))
0.0b
(sqrt (exp x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×sqrt-prod
5×*-un-lft-identity add-cube-cbrt
3×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2
1×fma-udef
Calls
3 calls:
Slowest
2.0ms
(sqrt (exp x))
2.0ms
(sqrt (exp x))
0.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x))))

series125.0ms

Calls
3 calls:
Slowest
87.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x))))
19.0ms
(sqrt (exp x))
19.0ms
(sqrt (exp x))

simplify383.0ms

Calls
17 calls:
Slowest
118.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
92.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
75.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
29.0ms
(- (exp x) (exp (* -1 x)))
23.0ms
(- (exp x) (exp (- x)))

prune458.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.2s3433×body1280valid
1.1s8031×body80valid
1.1s2481×body640valid
297.0ms1205×body320valid
140.0ms603×body160valid