Details

sample109.0ms

Algorithm

intervals

Results

88.0ms

630×

body

valid

simplify172.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

172.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

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

88.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
26.0ms	(* 4 (* b b))
21.0ms	(+ (* a a) (* b b))
16.0ms	(pow (+ (* a a) (* b b)) 2)

series243.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

98.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
52.0ms	(pow (+ (* a a) (* b b)) 2)
49.0ms	(* 4 (* b b))
44.0ms	(+ (* a a) (* b b))

simplify14.5s

Counts

88 → 92

Calls

88 calls:

Slowest

731.0ms	(* (* (+ (* a a) (* b b)) (+ (* a a) (* b b))) (+ (* a a) (* b b)))
516.0ms	(- (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
490.0ms	(- (* (pow (+ (* a a) (* b b)) 2) (pow (+ (* a a) (* b b)) 2)) (* (* 4 (* b b)) (* 4 (* b b))))
486.0ms	(* (* (* 4 (* b b)) (* 4 (* b b))) (* 4 (* b b)))
477.0ms	(+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b))))

prune909.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
0.5b	(* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))

rewrite13.0ms

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

9.0ms	(* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))
1.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(cbrt (fma b b (* a a)))
160.0ms	(cbrt (fma b b (* a a)))
154.0ms	(* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))
135.0ms	(cbrt (fma b b (* a a)))

simplify3.2s

Counts

111 → 97

Calls

111 calls:

Slowest

345.0ms	(* (* (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a))))) (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))))
219.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
171.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
171.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
167.0ms	(+ (pow a 4/3) (* 2/3 (* (pow (/ 1 (pow a 2)) 1/3) (pow b 2))))

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

Slowest

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

series571.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(cbrt (fma b b (* a a)))
152.0ms	(cbrt (fma b b (* a a)))
135.0ms	(cbrt (fma b b (* a a)))
132.0ms	(cbrt (fma b b (* a a)))

simplify2.2s

Counts

76 → 68

Calls

76 calls:

Slowest

209.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
207.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
188.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
187.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
82.0ms	(* (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) (cbrt (fma b b (* a a))))

prune1.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
9.8b	(sqrt (fma b b (* a a)))
9.8b	(sqrt (fma b b (* a a)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `fma-udef` `hypot-def`

Counts

4 → 62

Calls

4 calls:

Slowest

3.0ms	(sqrt (fma b b (* a a)))
2.0ms	(sqrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(cbrt (fma b b (* a a)))
146.0ms	(cbrt (fma b b (* a a)))
66.0ms	(sqrt (fma b b (* a a)))
58.0ms	(sqrt (fma b b (* a a)))

simplify1.8s

Counts

78 → 74

Calls

78 calls:

Slowest

193.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
172.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
88.0ms	(* (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (sqrt (fma b b (* a a))))
84.0ms	(* (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) (cbrt (fma b b (* a a))))
77.0ms	(* (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (sqrt (fma b b (* a a))))

prune1.1s

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 0.0b

regimes552.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.5s

20659×

body

valid