Details

Time bar (total: 41.2s)

sample483.0ms

Algorithm
halfpoints
Results

simplify194.0ms

Calls
1 calls:
Slowest
193.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize88.0ms

Local error

Found 3 expressions with local error:

58.4b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
3×insert-posit16
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod div-inv
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
11.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
11.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
5.0ms
(- (exp x) (exp (- x)))

series183.0ms

Calls
3 calls:
Slowest
84.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
59.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
40.0ms
(- (exp x) (exp (- x)))

simplify2.4s

Calls
33 calls:
Slowest
572.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
296.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
185.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
162.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
152.0ms
(* 1/2 (* (+ (exp x) (exp (- x))) (cos y)))

prune878.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/3 x)
0.1b
(* (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2) (sin y))
0.1b
(* x (* 1/3 x))
0.1b
(* (pow x 5) 1/60)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×associate-*r* *-commutative insert-posit16 add-log-exp
1×pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
17.0ms
(* (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2) (sin y))
5.0ms
(* (pow x 5) 1/60)
2.0ms
(* x (* 1/3 x))
0.0ms
(* 1/3 x)

series282.0ms

Calls
4 calls:
Slowest
143.0ms
(* (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2) (sin y))
71.0ms
(* (pow x 5) 1/60)
49.0ms
(* x (* 1/3 x))
19.0ms
(* 1/3 x)

simplify1.3s

Calls
24 calls:
Slowest
252.0ms
(* (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) (sin y))
195.0ms
(* (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2) (sin y))
181.0ms
(* (* (* (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2) (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (* (* (sin y) (sin y)) (sin y)))
128.0ms
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))
116.0ms
(+ (* 1/120 (* (pow x 5) (sin y))) (* 1/6 (* (pow x 3) (sin y))))

prune918.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
0.6b
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
0.6b
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
0.5b
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×cbrt-div pow1/3 associate-*r* associate-*l*
6×add-exp-log
5×div-inv
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))
2.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
2.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
2.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))

series1.1s

Calls
4 calls:
Slowest
338.0ms
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))
254.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
250.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
231.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))

simplify7.7s

Calls
53 calls:
Slowest
418.0ms
(+ (* (pow (cbrt 1/2) 2) (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ 1 x))))))) (+ (* 320/9 (/ (* (pow (cbrt 1/2) 2) (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ 1 x))))))) (pow x 4))) (* 40/3 (/ (* (pow (cbrt 1/2) 2) (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ 1 x))))))) (pow x 2)))))
382.0ms
(- (+ (* 1/18 (* (cbrt 1/2) (* (pow x 2) (exp (* 1/3 (+ (log 2) (log x))))))) (* (cbrt 1/2) (exp (* 1/3 (+ (log 2) (log x)))))) (* 1/3240 (* (cbrt 1/2) (* (pow x 4) (exp (* 1/3 (+ (log 2) (log x))))))))
380.0ms
(- (+ (* 1/18 (* (cbrt 1/2) (* (pow x 2) (exp (* 1/3 (+ (log 2) (log x))))))) (* (cbrt 1/2) (exp (* 1/3 (+ (log 2) (log x)))))) (* 1/3240 (* (cbrt 1/2) (* (pow x 4) (exp (* 1/3 (+ (log 2) (log x))))))))
371.0ms
(- (+ (* 20/3 (/ (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2)) (pow x 2))) (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2))) (* 40/9 (/ (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2)) (pow x 4))))
363.0ms
(+ (* (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ -1 x)))))) (pow (cbrt -1/2) 2)) (+ (* 40/3 (/ (* (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ -1 x)))))) (pow (cbrt -1/2) 2)) (pow x 2))) (* 320/9 (/ (* (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ -1 x)))))) (pow (cbrt -1/2) 2)) (pow x 4)))))

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))))
0.6b
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
0.6b
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
0.5b
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
19×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
8×cbrt-div
7×pow1/3 associate-*r* associate-*l*
6×add-exp-log
4×add-cbrt-cube insert-posit16 div-inv add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 frac-times flip3-+ pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-+
Calls
4 calls:
Slowest
10.0ms
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))
5.0ms
(cbrt (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))))
3.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
3.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))

series1.1s

Calls
4 calls:
Slowest
305.0ms
(* (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)) (cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2)))
302.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
256.0ms
(cbrt (/ (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))) 2))
214.0ms
(cbrt (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2))))

simplify7.9s

Calls
53 calls:
Slowest
523.0ms
(* (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2)))) (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* x (* 1/3 x)) 2)))))
396.0ms
(+ (* (pow (cbrt 1/2) 2) (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ 1 x))))))) (+ (* 320/9 (/ (* (pow (cbrt 1/2) 2) (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ 1 x))))))) (pow x 4))) (* 40/3 (/ (* (pow (cbrt 1/2) 2) (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ 1 x))))))) (pow x 2)))))
396.0ms
(- (+ (* 20/3 (/ (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2)) (pow x 2))) (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2))) (* 40/9 (/ (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2)) (pow x 4))))
374.0ms
(- (+ (* 20/3 (/ (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2)) (pow x 2))) (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2))) (* 40/9 (/ (* (exp (* 1/3 (- (log 1/60) (* 5 (log (/ -1 x)))))) (cbrt -1/2)) (pow x 4))))
367.0ms
(+ (* (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ -1 x)))))) (pow (cbrt -1/2) 2)) (+ (* 40/3 (/ (* (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ -1 x)))))) (pow (cbrt -1/2) 2)) (pow x 2))) (* 320/9 (/ (* (exp (* 1/3 (- (log 1/3600) (* 10 (log (/ -1 x)))))) (pow (cbrt -1/2) 2)) (pow x 4)))))

prune2.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch5.0ms

end0.0ms

sample11.8s

Algorithm
halfpoints
Results