Details

Time bar (total: 17.9s)

sample155.0ms

Algorithm
intervals
Results
86.0ms130×body1280valid
23.0ms56×body640valid
19.0ms266×body80valid
10.0ms38×body320valid
3.0ms20×body160valid

simplify86.0ms

Calls
1 calls:
Slowest
85.0ms
(/ (- (exp x) (exp (- x))) 2)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.4b

localize20.0ms

Local error

Found 1 expressions with local error:

5.8b
(- (exp x) (exp (- x)))

rewrite11.0ms

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
11.0ms
(- (exp x) (exp (- x)))

series57.0ms

Calls
1 calls:
Slowest
56.0ms
(- (exp x) (exp (- x)))

simplify1.2s

Calls
27 calls:
Slowest
120.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
86.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
83.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (exp (- x)) 1)))
76.0ms
(fma 1 (exp x) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
65.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (exp (- x)) 1)))

prune184.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (fma 1/3 (* x x) 2) x)
0.0b
(fma 1/3 (* x x) 2)
0.0b
(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×*-commutative
Calls
3 calls:
Slowest
3.0ms
(* (fma 1/3 (* x x) 2) x)
0.0ms
(fma 1/3 (* x x) 2)
0.0ms
(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

series272.0ms

Calls
3 calls:
Slowest
114.0ms
(* (fma 1/3 (* x x) 2) x)
80.0ms
(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))
78.0ms
(fma 1/3 (* x x) 2)

simplify616.0ms

Calls
11 calls:
Slowest
124.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
122.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
121.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
57.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))
48.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))

prune395.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (fma 1/3 (* x x) 2) x)))
0.0b
(* (fma 1/3 (* x x) 2) x)
0.0b
(* (fma 1/3 (* x x) 2) x)
0.0b
(fma 1/3 (* x x) 2)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*l*
9×pow1
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1/2 associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-prod-down pow-prod-up sqrt-prod
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp cbrt-unprod fma-udef
Calls
4 calls:
Slowest
18.0ms
(* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (fma 1/3 (* x x) 2) x)))
5.0ms
(* (fma 1/3 (* x x) 2) x)
4.0ms
(* (fma 1/3 (* x x) 2) x)
0.0ms
(fma 1/3 (* x x) 2)

series333.0ms

Calls
4 calls:
Slowest
101.0ms
(* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (fma 1/3 (* x x) 2) x)))
90.0ms
(* (fma 1/3 (* x x) 2) x)
89.0ms
(* (fma 1/3 (* x x) 2) x)
52.0ms
(fma 1/3 (* x x) 2)

simplify1.8s

Calls
34 calls:
Slowest
405.0ms
(* (* (* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (fma 1/3 (* x x) 2) x))) (sqrt (* (fma 1/3 (* x x) 2) x))) (* (* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (fma 1/3 (* x x) 2) x))) (sqrt (* (fma 1/3 (* x x) 2) x))))
162.0ms
(* (* (fma 1/3 (* x x) 2) x) (* (fma 1/3 (* x x) 2) x))
140.0ms
(* (* (fma 1/3 (* x x) 2) x) (* (fma 1/3 (* x x) 2) x))
71.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))
65.0ms
(sqrt (sqrt (* (fma 1/3 (* x x) 2) x)))

prune889.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

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))
0.3b
(* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (cbrt (fma 1/3 (* x x) 2))) x)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×pow1/2 pow-prod-down sqrt-prod
1×sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
60.0ms
(* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (* (* (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))

series651.0ms

Calls
4 calls:
Slowest
207.0ms
(cbrt (fma 1/3 (* x x) 2))
169.0ms
(cbrt (fma 1/3 (* x x) 2))
155.0ms
(cbrt (fma 1/3 (* x x) 2))
120.0ms
(* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (cbrt (fma 1/3 (* x x) 2))) x)))

simplify4.4s

Calls
33 calls:
Slowest
417.0ms
(- (+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (pow 2 1/3)) (* 1/324 (* (pow x 4) (pow 2 1/3))))
407.0ms
(- (+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (pow 2 1/3)) (* 1/324 (* (pow x 4) (pow 2 1/3))))
371.0ms
(- (+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (pow 2 1/3)) (* 1/324 (* (pow x 4) (pow 2 1/3))))
339.0ms
(* (* (* (sqrt (* (fma 1/3 (* x x) 2) x)) (sqrt (* (fma 1/3 (* x x) 2) x))) (sqrt (* (fma 1/3 (* x x) 2) x))) (* (* (sqrt (* (* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (cbrt (fma 1/3 (* x x) 2))) x)) (sqrt (* (* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (cbrt (fma 1/3 (* x x) 2))) x))) (sqrt (* (* (* (cbrt (fma 1/3 (* x x) 2)) (cbrt (fma 1/3 (* x x) 2))) (cbrt (fma 1/3 (* x x) 2))) x))))
339.0ms
(- (+ (* 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))))

prune988.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

0% (0.7b remaining)

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

bsearch2.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.7s3475×body1280valid
1.2s2356×body640valid
1.0s8203×body80valid
374.0ms1299×body320valid
102.0ms601×body160valid