Details

Time bar (total: 36.2s)

sample325.0ms

Algorithm
intervals
Results
159.0ms225×body10240exit
89.0ms109×body1280valid
44.0ms83×body640valid
11.0ms30×body320valid
5.0ms24×body160valid
1.0ms10×body80valid

simplify98.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
98.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.1b

localize14.0ms

Local error

Found 3 expressions with local error:

5.9b
(- (exp x) (exp (- x)))
0.5b
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
0.0b
(+ (exp x) (exp (- x)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
34×add-sqr-sqrt
22×add-cube-cbrt
20×times-frac
9×prod-diff
7×distribute-lft-out add-log-exp
6×distribute-lft-out-- difference-of-squares
5×add-cbrt-cube add-exp-log associate-/l*
4×associate-/r*
3×expm1-log1p-u pow1 fma-def fma-neg insert-posit16 log1p-expm1-u
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp tanh-undef div-inv
Counts
3 → 97
Calls
3 calls:
Slowest
59.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
12.0ms
(- (exp x) (exp (- x)))
9.0ms
(+ (exp x) (exp (- x)))

series194.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
115.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
54.0ms
(- (exp x) (exp (- x)))
26.0ms
(+ (exp x) (exp (- x)))

simplify6.0s

Counts
91 → 106
Calls
91 calls:
Slowest
431.0ms
(- (pow (exp x) 3) (pow (exp (- x)) 3))
318.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
270.0ms
(/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x)))
223.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
220.0ms
(fma 1 (exp x) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))

prune815.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b
(tanh x)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u tanh-def add-log-exp
Counts
1 → 13
Calls
1 calls:
Slowest
2.0ms
(tanh x)

series112.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
112.0ms
(tanh x)

simplify464.0ms

Counts
3 → 16
Calls
3 calls:
Slowest
268.0ms
(/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x)))
116.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
79.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

prune134.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b
(* x -1/3)
0.0b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0b
(fma 2/15 (pow x 5) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
5.0ms
(* x -1/3)
0.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0ms
(fma 2/15 (pow x 5) x)

series301.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
183.0ms
(fma 2/15 (pow x 5) x)
95.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
23.0ms
(* x -1/3)

simplify1.1s

Counts
18 → 52
Calls
18 calls:
Slowest
184.0ms
(* (* (* x x) x) (* (* -1/3 -1/3) -1/3))
169.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
164.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
151.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
119.0ms
(+ x (* 2/15 (pow x 5)))

prune483.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tanh x))
0.6b
(cbrt (tanh x))
0.6b
(cbrt (tanh x))
0.5b
(* (cbrt (tanh x)) (cbrt (tanh x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-div
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1 tanh-def
9×frac-times pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l/ associate-*r/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
Slowest
22.0ms
(* (cbrt (tanh x)) (cbrt (tanh x)))
2.0ms
(cbrt (tanh x))
2.0ms
(cbrt (tanh x))
1.0ms
(cbrt (tanh x))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
265.0ms
(* (cbrt (tanh x)) (cbrt (tanh x)))
264.0ms
(cbrt (tanh x))
257.0ms
(cbrt (tanh x))
251.0ms
(cbrt (tanh x))

simplify13.2s

Counts
98 → 121
Calls
98 calls:
Slowest
538.0ms
(pow (/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x))) 1/3)
411.0ms
(* (cbrt (- 1 (exp (* -2 x)))) (cbrt (tanh x)))
407.0ms
(* (cbrt (- (exp (* 2 x)) 1)) (cbrt (tanh x)))
379.0ms
(* (cbrt (- 1 (exp (* -2 x)))) (cbrt (- (exp (* 2 x)) 1)))
310.0ms
(* (* (cbrt (cbrt (tanh x))) (cbrt (cbrt (tanh x)))) (* (cbrt (cbrt (tanh x))) (cbrt (cbrt (tanh x)))))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

end0.0ms

sample10.6s

Algorithm
intervals
Results
6.0s7416×body10240exit
2.6s3368×body1280valid
1.3s2406×body640valid
342.0ms1200×body320valid
108.0ms599×body160valid
40.0ms427×body80valid