Details

sample134.0ms

Algorithm

intervals

Results

112.0ms

670×

body

valid

simplify198.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

198.0ms

(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
0.2b	(pow (+ (* a a) (* b b)) 2)
0.1b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
0.1b	(* (* a a) (- 1 a))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-r`
8×	`fma-def`
6×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `difference-of-squares` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 121

Calls

4 calls:

Slowest

68.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
35.0ms	(* (* b b) (+ 3 a))
26.0ms	(* (* a a) (- 1 a))
9.0ms	(pow (+ (* a a) (* b b)) 2)

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

166.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
78.0ms	(* (* a a) (- 1 a))
45.0ms	(* (* b b) (+ 3 a))
45.0ms	(pow (+ (* a a) (* b b)) 2)

simplify9.3s

Counts

83 → 133

Calls

83 calls:

Slowest

607.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
582.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
404.0ms	(- (+ (* 4 (pow a 2)) (* 12 (pow b 2))) (* 4 (pow a 3)))
359.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
342.0ms	(* 4 (* (* b b) (+ 3 a)))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize89.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(* (* a a) (* a a))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
36×	`pow-prod-up`
27×	`pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-r`
7×	`add-cube-cbrt`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
1×	`flip3-+` `swap-sqr` `flip-+` `distribute-lft-out`

Counts

4 → 127

Calls

4 calls:

Slowest

38.0ms	(* (* b b) (+ 3 a))
24.0ms	(* (* a a) (* a a))
6.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
82.0ms	(* b (fma b b (* 2 (* a a))))
67.0ms	(* (* a a) (* a a))
62.0ms	(* (* b b) (+ 3 a))

simplify5.6s

Counts

107 → 139

Calls

107 calls:

Slowest

766.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
382.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
367.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
316.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
302.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
0.1b	(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `fma-def` `distribute-lft-in`
2×	`associate-+r+` `flip3-+` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `sum-log` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

Slowest

36.0ms	(* (* b b) (+ 3 a))
8.0ms	(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
7.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series441.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

185.0ms	(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
117.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
97.0ms	(* b (fma b b (* 2 (* a a))))
42.0ms	(* (* b b) (+ 3 a))

simplify6.4s

Counts

46 → 93

Calls

46 calls:

Slowest

880.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
393.0ms	(sqrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
372.0ms	(* (* (* b b) (+ 3 a)) 4)
360.0ms	(* 4 (* (* b b) (+ 3 a)))
339.0ms	(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (+ a 3) (* b b))
0.1b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
0.0b	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`associate-*l/`
1×	`flip3-+` `associate-r` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

Slowest

40.0ms	(* (+ a 3) (* b b))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

175.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
112.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
87.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
70.0ms	(* (+ a 3) (* b b))

simplify3.4s

Counts

24 → 70

Calls

24 calls:

Slowest

486.0ms	(* (- (* a a) (* 3 3)) (* b b))
329.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
304.0ms	(- (+ (* 3 (pow b 2)) (* a (pow b 2))) (pow a 3))
293.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))
291.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch6.0ms

end0.0ms

sample5.0s

Algorithm

intervals

Results

4.6s

20567×

body

valid