Details

sample536.0ms

Algorithm

halfpoints

Results

simplify207.0ms

Calls

1 calls:

Slowest

206.0ms

(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.8b

localize89.0ms

Local error

Found 4 expressions with local error:

56.8b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
35×	`associate-l` `add-cube-cbrt`
29×	`times-frac`
25×	`associate-*l/`
14×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff` `associate-/l*`
8×	`pow1` `add-log-exp`
6×	`associate-/r` `associate-r*`
5×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr` `associate-/l/`
3×	`fma-def` `fma-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `div-inv` `flip--`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log`

Calls

4 calls:

Slowest

86.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
72.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
20.0ms	(+ (exp x) (exp (- x)))
13.0ms	(- (exp x) (exp (- x)))

series281.0ms

Calls

4 calls:

Slowest

118.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
87.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
48.0ms	(- (exp x) (exp (- x)))
27.0ms	(+ (exp x) (exp (- x)))

simplify10.1s

Calls

122 calls:

Slowest

860.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
448.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
410.0ms	(* (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (cos y))
369.0ms	(* (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (cos y))
359.0ms	(* (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (sin y))

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize136.0ms

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`associate-l`
28×	`add-cube-cbrt`
23×	`times-frac`
21×	`associate-*l/`
16×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-r`
7×	`associate-/l*`
6×	`associate-/r*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `*-commutative`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv` `associate-/l/`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`

Calls

4 calls:

Slowest

84.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
18.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
10.0ms	(+ (exp x) (exp (- x)))
6.0ms	(* x (fma 1/3 (* x x) 2))

series402.0ms

Calls

4 calls:

Slowest

156.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
121.0ms	(* x (fma 1/3 (* x x) 2))
76.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
48.0ms	(+ (exp x) (exp (- x)))

simplify13.1s

Calls

100 calls:

Slowest

770.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
738.0ms	(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
600.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
515.0ms	(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
506.0ms	(* (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

localize136.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin y) (/ 2 (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))))
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* x (fma 1/3 (* x x) 2))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
19×	`associate-/r` `associate-l*`
16×	`add-cbrt-cube` `add-exp-log`
12×	`associate-*l/`
10×	`associate-/l*`
9×	`associate-/r/`
8×	`pow1`
6×	`associate-r` `div-inv` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `fma-def` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`

Calls

4 calls:

Slowest

103.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
14.0ms	(/ (sin y) (/ 2 (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))))
10.0ms	(+ (exp x) (exp (- x)))
6.0ms	(* x (fma 1/3 (* x x) 2))

series459.0ms

Calls

4 calls:

Slowest

212.0ms	(/ (sin y) (/ 2 (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))))
108.0ms	(* x (fma 1/3 (* x x) 2))
99.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
40.0ms	(+ (exp x) (exp (- x)))

simplify30.5s

Calls

173 calls:

Slowest

889.0ms	(cbrt (/ 2 (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))))
783.0ms	(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
535.0ms	(/ 2 (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))))
528.0ms	(/ 2 (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))))
517.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))

prune3.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize128.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin y) (/ 2 (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))))
0.2b	(* 1/3 (* x x))
0.1b	(* x (* 1/3 (* x x)))
0.0b	(+ (exp x) (exp (- x)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
75×	`times-frac`
65×	`*-un-lft-identity`
64×	`associate-r`
63×	`add-cube-cbrt`
26×	`unswap-sqr`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`associate-/r*`
15×	`associate-l`
9×	`swap-sqr` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod`
8×	`*-commutative`
6×	`associate-/l*` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-exp`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Calls

4 calls:

Slowest

101.0ms	(* x (* 1/3 (* x x)))
37.0ms	(* 1/3 (* x x))
21.0ms	(/ (sin y) (/ 2 (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))))
10.0ms	(+ (exp x) (exp (- x)))

series330.0ms

Calls

4 calls:

Slowest

211.0ms	(/ (sin y) (/ 2 (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2)))))
59.0ms	(* x (* 1/3 (* x x)))
37.0ms	(* 1/3 (* x x))
24.0ms	(+ (exp x) (exp (- x)))

simplify30.0s

Calls

199 calls:

Slowest

604.0ms	(/ (sqrt (sin y)) (/ 2 (sqrt (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))))))
526.0ms	(* (* (* x x) x) (* (* (* 1/3 (* x x)) (* 1/3 (* x x))) (* 1/3 (* x x))))
520.0ms	(/ 1 (sqrt (/ 2 (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))))))
509.0ms	(/ (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))) 2)
505.0ms	(/ 2 (fma 1/60 (pow x 5) (+ (* x (* 1/3 (* x x))) (* x 2))))

prune4.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes217.0ms

Accuracy

0% (0.7b remaining)

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

bsearch7.0ms

end0.0ms

sample12.4s

Algorithm

halfpoints

Results