Details

sample100.0ms

Algorithm

intervals

Results

80.0ms

677×

body

valid

simplify236.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

236.0ms

(- (+ (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

localize29.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

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

1.0ms

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

series114.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

113.0ms

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

simplify683.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

284.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
265.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
133.0ms	(- (+ (pow a 4) (* 4 (pow b 2))) 1)

prune184.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))

rewrite16.0ms

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

8.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
6.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

327.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
269.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
244.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
216.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify14.0s

Counts

65 → 97

Calls

65 calls:

Slowest

477.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
474.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
412.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
395.0ms	(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
368.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))

rewrite20.0ms

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

15.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
1.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

351.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
248.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
230.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
221.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify14.1s

Counts

65 → 97

Calls

65 calls:

Slowest

660.0ms	(* (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
471.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
459.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
437.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
353.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.3b	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

rewrite3.0ms

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

series879.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

235.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
218.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
214.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
211.0ms	(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify4.1s

Counts

24 → 68

Calls

24 calls:

Slowest

475.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
411.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
401.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
385.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
314.0ms	(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes389.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.9s

20571×

body

valid