Details

sample93.0ms

Algorithm

intervals

Results

78.0ms

626×

body

valid

simplify254.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

254.0ms

(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (+ a 3) (* b b))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
0.0b	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`associate-*l/`
1×	`flip3-+` `associate-r` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

Slowest

28.0ms	(* (+ a 3) (* b b))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

137.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
111.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
66.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
46.0ms	(* (+ a 3) (* b b))

simplify2.7s

Counts

24 → 70

Calls

24 calls:

Slowest

323.0ms	(* (- (* a a) (* 3 3)) (* b b))
263.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))
234.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
230.0ms	(- (+ (* 3 (pow b 2)) (* a (pow b 2))) (pow a 3))
223.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune789.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(fma (* b b) 3 (* a a))
0.1b	(* a (* a a))
0.0b	(- (fma (* b b) 3 (* a a)) (* a (* a a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `associate--l+` `pow-sqr` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

Slowest

13.0ms	(* a (* a a))
10.0ms	(- (fma (* b b) 3 (* a a)) (* a (* a a)))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (* b b) 3 (* a a))

series225.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
48.0ms	(- (fma (* b b) 3 (* a a)) (* a (* a a)))
45.0ms	(* a (* a a))
41.0ms	(fma (* b b) 3 (* a a))

simplify2.5s

Counts

36 → 83

Calls

36 calls:

Slowest

432.0ms	(* (* (* a a) a) (* (* (* a a) a) (* (* a a) a)))
399.0ms	(* (* (* a a) a) (* (* (* a a) (* a a)) (* a a)))
219.0ms	(/ (exp (fma (* b b) 3 (* a a))) (exp (* a (* a a))))
185.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
184.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune711.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

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

series618.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
153.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
148.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
147.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

simplify7.6s

Counts

65 → 97

Calls

65 calls:

Slowest

411.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
257.0ms	(* (sqrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (sqrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
235.0ms	(* (cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
204.0ms	(* (cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
199.0ms	(* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

prune895.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -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 b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series583.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
145.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
145.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
144.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

simplify1.5s

Counts

24 → 68

Calls

24 calls:

Slowest

167.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
166.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
166.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
165.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
165.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

prune730.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.8s

20385×

body

valid