Details

Time bar (total: 2.5m)

sample438.0ms

Algorithm
halfpoints
Results

simplify269.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
268.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize120.0ms

Local error

Found 4 expressions with local error:

57.4b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b
(+ (exp x) (exp (- x)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
47×*-un-lft-identity
35×associate-*l*
31×add-cube-cbrt
29×times-frac
14×add-cbrt-cube add-exp-log
9×prod-diff
8×pow1 add-log-exp
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
3×fma-def fma-neg
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 126
Calls
4 calls:
Slowest
72.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
44.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
21.0ms
(- (exp x) (exp (- x)))
10.0ms
(+ (exp x) (exp (- x)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
85.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
56.0ms
(- (exp x) (exp (- x)))
32.0ms
(+ (exp x) (exp (- x)))

simplify7.6s

Counts
99 → 138
Calls
99 calls:
Slowest
795.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
492.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
412.0ms
(+ (log (/ (+ (exp x) (exp (- x))) 2)) (log (cos y)))
276.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
272.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize148.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
0.0b
(* x (fma 1/3 (* x x) 2))
0.0b
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
32×associate-*l*
29×*-un-lft-identity
23×times-frac add-cube-cbrt
16×add-cbrt-cube add-exp-log
10×pow1
9×associate-*r*
5×prod-exp cbrt-unprod unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative fma-udef distribute-lft-out
2×cbrt-undiv div-exp associate-*l/ div-inv
1×distribute-rgt-in distribute-lft-in
Counts
4 → 107
Calls
4 calls:
Slowest
52.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
19.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
5.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
110.0ms
(* x (fma 1/3 (* x x) 2))
90.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
86.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

simplify10.8s

Counts
77 → 119
Calls
77 calls:
Slowest
751.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
547.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
469.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
446.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
434.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize115.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt 2))
0.4b
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.3b
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
0.2b
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
54×add-exp-log
44×associate-*l*
43×sqrt-prod
34×add-cbrt-cube
22×prod-exp
14×div-exp
13×pow1
12×associate-/r* cbrt-unprod
8×cbrt-undiv
6×associate-/l*
4×expm1-log1p-u rec-exp 1-exp associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-flip unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times sqrt-pow1 pow1/2 associate-*r/ inv-pow
Counts
4 → 192
Calls
4 calls:
Slowest
44.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
19.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
11.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
5.0ms
(/ 1 (sqrt 2))

series638.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
260.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
201.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
177.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ 1 (sqrt 2))

simplify28.8s

Counts
187 → 202
Calls
187 calls:
Slowest
814.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (cbrt (sqrt 2)))
755.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
643.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
617.0ms
(/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
532.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt (cbrt 2)))

prune4.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize144.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
1.0b
(/ 1 (sqrt (sqrt 2)))
0.4b
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.3b
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))

rewrite566.0ms

Algorithm
rewrite-expression-head
Rules
1128×sqrt-prod
1116×times-frac
592×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
283×associate-*l*
79×add-exp-log
49×add-cbrt-cube
37×associate-/l*
32×div-exp
25×prod-exp
24×associate-/r*
23×pow1 div-inv
20×sqrt-pow1
17×cbrt-undiv
15×cbrt-unprod
14×pow-flip
10×pow1/2 pow-div
5×rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*l/
2×inv-pow
1×frac-times associate-*r* associate-*r/ *-commutative associate-/l/
Counts
4 → 777
Calls
4 calls:
Slowest
104.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
11.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
7.0ms
(/ 1 (sqrt (sqrt 2)))

series501.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
306.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
194.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify1.0m

Counts
1058 → 785
Calls
1058 calls:
Slowest
1.1s
(* (/ (/ (* (* 1 1) 1) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
955.0ms
(* (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
942.0ms
(* (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
900.0ms
(* (* (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
860.0ms
(* (/ (/ (* (* 1 1) 1) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))

prune19.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

48% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.9b

bsearch193.0ms

end0.0ms

sample12.4s

Algorithm
halfpoints
Results