Details

sample94.0ms

Algorithm

intervals

Results

72.0ms

640×

body

valid

simplify937.0ms

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

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

series302.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(fma (* 4 b) b (fma (fma b b (* a a)) (fma b b (* a a)) -1))
93.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
48.0ms	(fma b b (* a a))
43.0ms	(fma b b (* a a))

simplify1.9s

Counts: 56 → 56

prune610.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b	(* 4 (* b b))
0.0b	(+ (* a a) (* b b))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`fma-def` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
8×	`add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

Slowest

78.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
13.0ms	(* 4 (* b b))
9.0ms	(+ (* a a) (* b b))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series254.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
63.0ms	(pow (+ (* a a) (* b b)) 2)
49.0ms	(+ (* a a) (* b b))
48.0ms	(* 4 (* b b))

simplify1.6s

Counts: 92 → 92

prune906.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (fma b b (* a a)))
8.3b	(cbrt (fma b b (* a a)))
8.3b	(cbrt (fma b b (* a a)))
0.5b	(* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

13.0ms	(* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))
2.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))
152.0ms	(cbrt (fma b b (* a a)))
145.0ms	(cbrt (fma b b (* a a)))
138.0ms	(cbrt (fma b b (* a a)))

simplify1.1s

Counts: 97 → 97

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

18.7b	(cbrt (* (fma b b (* a a)) (fma b b (* a a))))
8.3b	(cbrt (fma b b (* a a)))
0.3b	(* (fma b b (* a a)) (fma b b (* a a)))
0.3b	(* (cbrt (* (fma b b (* a a)) (fma b b (* a a)))) (cbrt (fma b b (* a a))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`cbrt-prod` `pow1`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log`
7×	`associate-l`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow1/3` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `pow-prod-down`
2×	`prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow3` `pow-sqr` `pow-prod-up`

Counts

4 → 86

Calls

4 calls:

Slowest

20.0ms	(* (fma b b (* a a)) (fma b b (* a a)))
20.0ms	(* (cbrt (* (fma b b (* a a)) (fma b b (* a a)))) (cbrt (fma b b (* a a))))
6.0ms	(cbrt (* (fma b b (* a a)) (fma b b (* a a))))
1.0ms	(cbrt (fma b b (* a a)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

190.0ms	(cbrt (* (fma b b (* a a)) (fma b b (* a a))))
140.0ms	(cbrt (fma b b (* a a)))
66.0ms	(* (fma b b (* a a)) (fma b b (* a a)))
64.0ms	(* (cbrt (* (fma b b (* a a)) (fma b b (* a a)))) (cbrt (fma b b (* a a))))

simplify860.0ms

Counts: 98 → 98

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes599.0ms

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

20483×

body

valid