Details

Time bar (total: 36.2s)

sample226.0ms

Algorithm
intervals
Results
126.0ms254×body10240exit
62.0ms130×body1280valid
17.0ms56×body640valid
8.0ms38×body320valid
2.0ms19×body160valid
1.0ms13×body80valid

simplify55.0ms

Calls
1 calls:
Slowest
55.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.4b

localize23.0ms

Local error

Found 2 expressions with local error:

5.8b
(- (exp x) (exp (- x)))
0.0b
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
25×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out distribute-lft-out-- difference-of-squares
5×associate-/l*
4×associate-/r* add-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp tanh-undef flip-+ div-inv
Calls
2 calls:
Slowest
38.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
10.0ms
(- (exp x) (exp (- x)))

series153.0ms

Calls
2 calls:
Slowest
110.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
43.0ms
(- (exp x) (exp (- x)))

simplify3.1s

Calls
64 calls:
Slowest
387.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
233.0ms
(- (pow (exp x) 3) (pow (exp (- x)) 3))
226.0ms
(/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x)))
223.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
170.0ms
(/ (* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x)))) (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))))

prune361.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(tanh x)

rewrite2.0ms

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

series117.0ms

Calls
1 calls:
Slowest
116.0ms
(tanh x)

simplify613.0ms

Calls
3 calls:
Slowest
286.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
257.0ms
(/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x)))
69.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

prune102.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x x) -1/3)
0.1b
(* (* (* x x) -1/3) x)
0.1b
(* (pow x 5) 2/15)
0.0b
(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-cbrt-cube
18×pow1
15×add-sqr-sqrt
12×prod-exp
10×cbrt-unprod
9×*-un-lft-identity associate-*r* associate-*l* pow-prod-down add-cube-cbrt add-log-exp
4×unpow-prod-down insert-posit16 unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×pow-to-exp +-commutative associate-+l+ flip3-+ pow-exp flip-+
Calls
4 calls:
Slowest
293.0ms
(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
48.0ms
(* (* (* x x) -1/3) x)
16.0ms
(* (* x x) -1/3)
11.0ms
(* (pow x 5) 2/15)

series270.0ms

Calls
4 calls:
Slowest
91.0ms
(* (pow x 5) 2/15)
70.0ms
(* (* (* x x) -1/3) x)
59.0ms
(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
51.0ms
(* (* x x) -1/3)

simplify4.6s

Calls
55 calls:
Slowest
655.0ms
(* (* (* (* (* x x) -1/3) (* (* x x) -1/3)) (* (* x x) -1/3)) (* (* x x) x))
439.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
394.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
355.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
276.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/3 -1/3) -1/3))

prune756.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite31.0ms

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×add-cbrt-cube insert-posit16 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
Calls
4 calls:
Slowest
25.0ms
(* (cbrt (tanh x)) (cbrt (tanh x)))
2.0ms
(cbrt (tanh x))
1.0ms
(cbrt (tanh x))
1.0ms
(cbrt (tanh x))

series1.0s

Calls
4 calls:
Slowest
267.0ms
(cbrt (tanh x))
266.0ms
(cbrt (tanh x))
253.0ms
(* (cbrt (tanh x)) (cbrt (tanh x)))
248.0ms
(cbrt (tanh x))

simplify12.4s

Calls
98 calls:
Slowest
715.0ms
(* (cbrt (- 1 (exp (* -2 x)))) (cbrt (- (exp (* 2 x)) 1)))
420.0ms
(* (cbrt (- 1 (exp (* -2 x)))) (cbrt (tanh x)))
362.0ms
(* (cbrt (- (exp (* 2 x)) 1)) (cbrt (tanh x)))
330.0ms
(* (cbrt (- (exp (* 2 x)) 1)) (cbrt (- 1 (exp (* -2 x)))))
297.0ms
(* (* (cbrt (cbrt (tanh x))) (cbrt (cbrt (tanh x)))) (* (cbrt (cbrt (tanh x))) (cbrt (cbrt (tanh x)))))

prune977.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (1.8b remaining)

Error of 1.8b against oracle of 0.0b and baseline of 1.8b

bsearch2.0ms

end0.0ms

sample10.8s

Algorithm
intervals
Results
5.3s7623×body10240exit
3.3s3417×body1280valid
1.4s2313×body640valid
387.0ms1266×body320valid
132.0ms594×body160valid
38.0ms410×body80valid