Details

Time bar (total: 1.2m)

sample504.0ms

Algorithm
halfpoints
Results

simplify192.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
192.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.2b

localize130.0ms

Local error

Found 4 expressions with local error:

58.0b
(- (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)))

rewrite189.0ms

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
74.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
56.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
35.0ms
(- (exp x) (exp (- x)))
21.0ms
(+ (exp x) (exp (- x)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
94.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
83.0ms
(- (exp x) (exp (- x)))
28.0ms
(+ (exp x) (exp (- x)))

simplify7.4s

Counts
99 → 138
Calls
99 calls:
Slowest
782.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
425.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
308.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
282.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
251.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize133.0ms

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

rewrite71.0ms

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
50.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
13.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
6.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* x (fma 1/3 (* x x) 2))
126.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
92.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
74.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

simplify11.2s

Counts
77 → 119
Calls
77 calls:
Slowest
785.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
534.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
489.0ms
(* (cbrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (cbrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)))
477.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
477.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize148.0ms

Local error

Found 4 expressions with local error:

0.5b
(* x (sqrt (fma 1/3 (* x x) 2)))
0.4b
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
0.1b
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
33×associate-*l*
32×*-un-lft-identity
26×add-cube-cbrt
23×times-frac
21×add-cbrt-cube add-exp-log
18×associate-*r*
15×pow1
8×prod-exp cbrt-unprod
7×sqrt-prod
6×pow-prod-down unswap-sqr
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-out
2×cbrt-undiv div-exp associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
Slowest
53.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
24.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
19.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
8.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
195.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
119.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
111.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
73.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify9.3s

Counts
92 → 134
Calls
92 calls:
Slowest
501.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
471.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
345.0ms
(* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sin y))
240.0ms
(* (/ (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))) (* (* 2 2) 2)) (* (* (cos y) (cos y)) (cos y)))
238.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize135.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt 2))
0.5b
(* x (sqrt (fma 1/3 (* x x) 2)))
0.4b
(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))
0.4b
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2)) (sin y)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt times-frac
51×add-exp-log
50×*-un-lft-identity add-cube-cbrt
37×sqrt-prod
31×add-cbrt-cube
25×associate-*l*
21×prod-exp
13×pow1 div-exp
12×associate-/r*
11×cbrt-unprod
7×cbrt-undiv associate-*r*
6×associate-/l*
4×expm1-log1p-u rec-exp 1-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ div-inv pow-flip
2×clear-num frac-2neg *-commutative unswap-sqr
1×frac-times sqrt-pow1 pow1/2 associate-*r/ inv-pow
Counts
4 → 172
Calls
4 calls:
Slowest
76.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2)) (sin y)))
8.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
6.0ms
(/ 1 (sqrt 2))
5.0ms
(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))

series618.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
273.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2)) (sin y)))
193.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
152.0ms
(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))
0.0ms
(/ 1 (sqrt 2))

simplify18.3s

Counts
166 → 182
Calls
166 calls:
Slowest
773.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
702.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
701.0ms
(+ (* 1/60 (/ (* (pow x 5) (sin y)) (pow (sqrt 2) 2))) (* 1/3 (/ (* (pow x 3) (sin y)) (pow (sqrt 2) 2))))
565.0ms
(/ (* (* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
542.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2)) (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))) (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))

prune4.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes154.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch4.0ms

end0.0ms

sample12.3s

Algorithm
halfpoints
Results