Details

Time bar (total: 38.3s)

sample206.0ms

Algorithm
intervals
Results
105.0ms110×body1280valid
41.0ms81×body640valid
26.0ms284×body80valid
12.0ms34×body320valid
6.0ms20×body160valid

simplify65.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
65.0ms
(/ (- (exp x) (exp (- x))) 2)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.6b

localize34.0ms

Local error

Found 1 expressions with local error:

5.3b
(- (exp x) (exp (- x)))

rewrite27.0ms

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
Counts
1 → 29
Calls
1 calls:
Slowest
26.0ms
(- (exp x) (exp (- x)))

series68.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
68.0ms
(- (exp x) (exp (- x)))

simplify2.3s

Counts
27 → 32
Calls
27 calls:
Slowest
344.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
236.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
211.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
184.0ms
(fma 1 (exp x) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
144.0ms
(fma (- (cbrt (exp (- x)))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))) (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x))))))

prune319.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×fma-udef
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 45
Calls
3 calls:
Slowest
8.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/3 (* x x) 2)
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series296.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
121.0ms
(* x (fma 1/3 (* x x) 2))
88.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
86.0ms
(fma 1/3 (* x x) 2)

simplify2.6s

Counts
21 → 54
Calls
21 calls:
Slowest
859.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
413.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
323.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
261.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
142.0ms
(+ (* 2 x) (* 1/3 (pow x 3)))

prune488.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/3 (* x x))
0.1b
(* x (* 1/3 (* x x)))
0.0b
(+ (* x (* 1/3 (* x x))) (* x 2))
0.0b
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt
6×*-un-lft-identity associate-*l* add-cube-cbrt add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×associate-*r* *-commutative
1×+-commutative sum-log fma-def flip3-+ flip-+ fma-udef distribute-lft-out unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
53.0ms
(* x (* 1/3 (* x x)))
45.0ms
(+ (* x (* 1/3 (* x x))) (* x 2))
14.0ms
(* 1/3 (* x x))
0.0ms
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(+ (* x (* 1/3 (* x x))) (* x 2))
84.0ms
(fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))
47.0ms
(* x (* 1/3 (* x x)))
39.0ms
(* 1/3 (* x x))

simplify4.1s

Counts
36 → 85
Calls
36 calls:
Slowest
579.0ms
(* (* (* x x) x) (* (* (* 1/3 (* x x)) (* 1/3 (* x x))) (* 1/3 (* x x))))
486.0ms
(* (* (* x x) x) (* (* (* 1/3 1/3) 1/3) (* (* (* x x) (* x x)) (* x x))))
469.0ms
(* (* (* x x) x) (* (* (* 1/3 1/3) 1/3) (* (* (* x x) x) (* (* x x) x))))
291.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
281.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))

prune937.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

5.3b
(- (exp x) (exp (- x)))
5.3b
(- (exp x) (exp (- x)))
5.3b
(- (exp x) (exp (- x)))
0.1b
(cbrt (* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x)))))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt *-un-lft-identity
30×flip3-- flip--
28×frac-times
27×prod-diff
26×cbrt-div
25×add-cube-cbrt
14×associate-*l/
10×add-log-exp
9×fma-neg
8×associate-*r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sub-neg diff-log distribute-lft-out-- difference-of-squares
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 126
Calls
4 calls:
Slowest
160.0ms
(cbrt (* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x)))))
30.0ms
(- (exp x) (exp (- x)))
26.0ms
(- (exp x) (exp (- x)))
25.0ms
(- (exp x) (exp (- x)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
54.0ms
(cbrt (* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x)))))
51.0ms
(- (exp x) (exp (- x)))
45.0ms
(- (exp x) (exp (- x)))
44.0ms
(- (exp x) (exp (- x)))

simplify19.0s

Counts
112 → 138
Calls
112 calls:
Slowest
1.1s
(cbrt (* (* (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))) (- (exp x) (exp (- x)))))
1.0s
(cbrt (* (* (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (- (exp x) (exp (- x)))) (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))))
1.0s
(cbrt (* (* (- (pow (exp x) 3) (pow (exp (- x)) 3)) (- (pow (exp x) 3) (pow (exp (- x)) 3))) (- (pow (exp x) 3) (pow (exp (- x)) 3))))
930.0ms
(cbrt (* (* (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))) (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))))
686.0ms
(cbrt (* (* (- (pow (exp x) 3) (pow (exp (- x)) 3)) (- (pow (exp x) 3) (pow (exp (- x)) 3))) (- (exp x) (exp (- x)))))

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.3s3362×body1280valid
1.7s2527×body640valid
786.0ms8258×body80valid
362.0ms1175×body320valid
112.0ms636×body160valid