Details

sample77.0ms

Algorithm

intervals

Results

57.0ms

661×

body

valid

simplify219.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

219.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0b	(fma (* b b) 4 -1)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 22

Calls

2 calls:

Slowest

0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (* b b) 4 -1)

series213.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

142.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
71.0ms	(fma (* b b) 4 -1)

simplify693.0ms

Counts

6 → 28

Calls

6 calls:

Slowest

283.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
272.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
42.0ms	(- (* 4 (pow b 2)) 1)
35.0ms	(- (* 4 (pow b 2)) 1)
31.0ms	(- (* 4 (pow b 2)) 1)

prune333.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

Slowest

1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1)))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

series605.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

248.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1)))
131.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
117.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
110.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

simplify3.2s

Counts

15 → 59

Calls

15 calls:

Slowest

364.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
341.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
338.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
301.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))))
284.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune771.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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

4 → 44

Calls

4 calls:

Slowest

1.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

series506.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
132.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
125.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
117.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

simplify2.6s

Counts

12 → 56

Calls

12 calls:

Slowest

362.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
308.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
304.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
296.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
296.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune910.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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

4 → 44

Calls

4 calls:

Slowest

0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

series920.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

543.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
142.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
130.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))
105.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

simplify2.7s

Counts

12 → 56

Calls

12 calls:

Slowest

357.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
331.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
323.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
310.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
309.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.1b

regimes289.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

3.0s

20639×

body

valid