Details

sample189.0ms

Algorithm

intervals

Results

161.0ms

630×

body

valid

simplify146.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

145.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (+ a 3) (* b b))
0.1b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0b	(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))

rewrite57.0ms

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

55.0ms	(* (+ 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)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
98.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
71.0ms	(* (+ a 3) (* b b))
65.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))

simplify13.1s

Counts

70 → 70

Calls

70 calls:

Slowest

824.0ms	(* (* (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
454.0ms	(* (* (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma a (* (- 1 a) a) (* (+ a 3) (* b b)))) (fma a (* (- 1 a) a) (* (+ a 3) (* b b))))
387.0ms	(* (* (fma (fma b b (* a a)) (fma b b (* a a)) -1) (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
378.0ms	(* (- (* a a) (* 3 3)) (* b b))
359.0ms	(* 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))))

prune994.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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

14.0ms	(* a (* a a))
10.0ms	(- (fma (* b b) 3 (* a a)) (* a (* a a)))
0.0ms	(fma (* b b) 3 (* a a))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series275.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
72.0ms	(- (fma (* b b) 3 (* a a)) (* a (* a a)))
56.0ms	(* a (* a a))
43.0ms	(fma (* b b) 3 (* a a))

simplify13.0s

Counts

87 → 83

Calls

87 calls:

Slowest

668.0ms	(* (* (fma (fma b b (* a a)) (fma b b (* a a)) -1) (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
629.0ms	(* (* (* a a) a) (* (* (* a a) a) (* (* a a) a)))
496.0ms	(* (* (* a (* a a)) (* a (* a a))) (* a (* a a)))
477.0ms	(- (pow (fma (* b b) 3 (* a a)) 3) (pow (* a (* a a)) 3))
404.0ms	(+ (* (fma (* b b) 3 (* a a)) (fma (* b b) 3 (* a a))) (+ (* (* a (* a a)) (* a (* a a))) (* (fma (* b b) 3 (* a a)) (* a (* a a)))))

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (+ a 3) (* b b))
0.8b	(* (+ a 3) (* b b))
0.8b	(* (+ a 3) (* b b))
0.2b	(cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

Slowest

42.0ms	(* (+ a 3) (* b b))
32.0ms	(* (+ a 3) (* b b))
27.0ms	(* (+ a 3) (* b b))
2.0ms	(cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

209.0ms	(cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
74.0ms	(* (+ a 3) (* b b))
65.0ms	(* (+ a 3) (* b b))
52.0ms	(* (+ a 3) (* b b))

simplify10.1s

Counts

103 → 101

Calls

103 calls:

Slowest

415.0ms	(* (- (* a a) (* 3 3)) (* b b))
362.0ms	(* (- (* a a) (* 3 3)) (* b b))
356.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow a 2) (pow -1 1/3))) (* 4 (* (pow b 2) (pow -1 1/3)))))
300.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))
284.0ms	(* (* (cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))) (cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (+ a 3) (* b b))
0.8b	(* (+ a 3) (* b b))
0.8b	(* (+ a 3) (* b b))
0.8b	(* (+ a 3) (* b b))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`-un-lft-identity` `associate-l*`
12×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`associate-*l/` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `*-commutative` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

Slowest

31.0ms	(* (+ a 3) (* b b))
28.0ms	(* (+ a 3) (* b b))
27.0ms	(* (+ a 3) (* b b))
25.0ms	(* (+ a 3) (* b b))

series198.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

53.0ms	(* (+ a 3) (* b b))
50.0ms	(* (+ a 3) (* b b))
48.0ms	(* (+ a 3) (* b b))
47.0ms	(* (+ a 3) (* b b))

simplify6.3s

Counts

112 → 112

Calls

112 calls:

Slowest

314.0ms	(expm1 (* (+ a 3) (* b b)))
304.0ms	(* (- (* a a) (* 3 3)) (* b b))
245.0ms	(* (- (* a a) (* 3 3)) (* b b))
242.0ms	(* (- (* a a) (* 3 3)) (* b b))
241.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes113.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.2s

20659×

body

valid