Details

sample124.0ms

Algorithm

intervals

Results

107.0ms

617×

body

valid

simplify194.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

194.0ms

(- (+ (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

localize67.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (+ a 3) (* b b))
0.2b	(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	(* (- 1 a) a)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`associate-l`
7×	`add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `fma-udef` `difference-of-squares` `unswap-sqr`
1×	`flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 73

Calls

4 calls:

Slowest

38.0ms	(* (+ a 3) (* b b))
30.0ms	(* (- 1 a) a)
1.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series295.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

106.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
84.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
53.0ms	(* (- 1 a) a)
52.0ms	(* (+ a 3) (* b b))

simplify3.1s

Counts

37 → 85

Calls

37 calls:

Slowest

415.0ms	(* (- (* a a) (* 3 3)) (* b b))
284.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
261.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
247.0ms	(- (+ (* 3 (pow b 2)) (* a (pow b 2))) (pow a 3))
239.0ms	(* (- (pow 1 3) (pow a 3)) a)

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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

40.0ms	(* (+ a 3) (* b b))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series377.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
110.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
102.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
52.0ms	(* (+ a 3) (* b b))

simplify2.8s

Counts

24 → 70

Calls

24 calls:

Slowest

351.0ms	(* (- (* a a) (* 3 3)) (* b b))
338.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))
272.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
268.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
262.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

13.7b	(cbrt (* (* (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)))
0.8b	(* (+ a 3) (* b b))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

rewrite40.0ms

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`
2×	`associate-*l/` `fma-udef`
1×	`cbrt-prod` `flip3-+` `pow1/3` `associate-r` `pow3` `*-commutative` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

Slowest

28.0ms	(* (+ a 3) (* b b))
10.0ms	(cbrt (* (* (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)))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series709.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

491.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
86.0ms	(cbrt (* (* (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)))
80.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
51.0ms	(* (+ a 3) (* b b))

simplify2.7s

Counts

26 → 72

Calls

26 calls:

Slowest

277.0ms	(* (- (* a a) (* 3 3)) (* b b))
269.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
258.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
243.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
239.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))

prune938.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

13.7b	(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)) (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)))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.8b	(* (+ a 3) (* b b))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

rewrite217.0ms

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`
2×	`associate-*l/` `fma-udef`
1×	`cbrt-prod` `flip3-+` `pow1/3` `associate-r` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

Slowest

186.0ms	(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)) (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)))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
31.0ms	(* (+ a 3) (* b b))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series344.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
97.0ms	(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)) (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)))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
91.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
47.0ms	(* (+ a 3) (* b b))

simplify2.8s

Counts

25 → 71

Calls

25 calls:

Slowest

380.0ms	(* (- (* a a) (* 3 3)) (* b b))
250.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))
246.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
245.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
230.0ms	(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)) (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)))))

prune1.1s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.1b

regimes134.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.8s

20417×

body

valid