Details

sample76.0ms

Algorithm

intervals

Results

62.0ms

670×

body

valid

simplify170.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

170.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

Slowest

0.0ms

(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))

series117.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

117.0ms

(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))

simplify799.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

326.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
309.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
163.0ms	(- (+ (pow a 4) (* 4 (pow b 2))) 1)

prune170.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 1 expressions with local error:

0.2b	(* (fma a a (* b b)) (fma a a (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
3×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
2×	`fma-udef`
1×	`pow2` `distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 30

Calls

1 calls:

Slowest

7.0ms

(* (fma a a (* b b)) (fma a a (* b b)))

series62.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

61.0ms

(* (fma a a (* b b)) (fma a a (* b b)))

simplify1.9s

Counts

26 → 33

Calls

26 calls:

Slowest

494.0ms	(* (* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b))) (* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b))))
331.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
244.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
232.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
131.0ms	(* (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))))

prune386.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

9.3b	(sqrt (fma a a (* b b)))
9.3b	(sqrt (fma a a (* b b)))
0.2b	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
0.2b	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
19×	`add-sqr-sqrt`
15×	`pow-prod-up`
13×	`sqrt-prod`
12×	`sqrt-pow1` `pow1/2` `associate-l`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`fma-udef`
6×	`pow-plus`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `cube-unmult` `*-commutative` `hypot-def` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

Slowest

29.0ms	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
9.0ms	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
7.0ms	(sqrt (fma a a (* b b)))
2.0ms	(sqrt (fma a a (* b b)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
59.0ms	(sqrt (fma a a (* b b)))
53.0ms	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
51.0ms	(sqrt (fma a a (* b b)))

simplify4.6s

Counts

79 → 115

Calls

79 calls:

Slowest

776.0ms	(* (* (* (sqrt (fma a a (* b b))) (sqrt (fma a a (* b b)))) (sqrt (fma a a (* b b)))) (* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b))))
357.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
328.0ms	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
326.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
302.0ms	(- (+ (* 3/2 (* a (pow b 2))) (pow a 3)))

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (hypot a b) 4)
0.0b	(hypot a b)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`pow1` `pow-unpow` `unpow-prod-down` `add-exp-log`
2×	`expm1-log1p-u` `hypot-udef` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

2 → 32

Calls

2 calls:

Slowest

5.0ms	(pow (hypot a b) 4)
0.0ms	(hypot a b)

series169.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

102.0ms	(pow (hypot a b) 4)
67.0ms	(hypot a b)

simplify947.0ms

Counts

14 → 38

Calls

14 calls:

Slowest

297.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
287.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
249.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
74.0ms	(pow (* (cbrt (hypot a b)) (cbrt (hypot a b))) 4)
14.0ms	(pow (sqrt (hypot a b)) 4)

prune462.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes82.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.2s

20567×

body

valid