Details

sample121.0ms

Algorithm

intervals

Results

94.0ms

640×

body

valid

simplify839.0ms

Counts: 1 → 1

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* b b) (- 1 (* 3 a)))
0.3b	(pow (+ (* a a) (* b b)) 2)
0.1b	(* (* a a) (+ 1 a))
0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))

rewrite584.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
8×	`fma-def`
7×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

Slowest

453.0ms	(* (* a a) (+ 1 a))
94.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
26.0ms	(* (* b b) (- 1 (* 3 a)))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series356.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

175.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
79.0ms	(* (* a a) (+ 1 a))
61.0ms	(* (* b b) (- 1 (* 3 a)))
40.0ms	(pow (+ (* a a) (* b b)) 2)

simplify699.0ms

Counts: 118 → 118

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize91.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* a a) (* b b))
0.7b	(* (* b b) (- 1 (* 3 a)))
0.2b	(* (* a a) (* a a))
0.1b	(fma (* b b) (* b b) (fma (* (* a a) (* b b)) 2 (* (* a a) (* a a))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

148×	`pow1`
40×	`pow-prod-down` `pow-prod-up`
33×	`add-cbrt-cube` `add-exp-log`
24×	`pow-sqr`
22×	`pow-plus`
19×	`prod-exp` `cbrt-unprod`
15×	`pow2`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `swap-sqr` `fma-udef` `flip--`

Counts

4 → 143

Calls

4 calls:

Slowest

27.0ms	(* (* b b) (- 1 (* 3 a)))
23.0ms	(* (* a a) (* b b))
23.0ms	(* (* a a) (* a a))
0.0ms	(fma (* b b) (* b b) (fma (* (* a a) (* b b)) 2 (* (* a a) (* a a))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(fma (* b b) (* b b) (fma (* (* a a) (* b b)) 2 (* (* a a) (* a a))))
73.0ms	(* (* b b) (- 1 (* 3 a)))
62.0ms	(* (* a a) (* a a))
47.0ms	(* (* a a) (* b b))

simplify2.4s

Counts: 155 → 155

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* a a) (* b b))
0.7b	(* (* b b) (- 1 (* 3 a)))
0.1b	(fma (* b b) (* b b) (fma (* (* a a) (* b b)) 2 (pow a 4)))
0.1b	(* (* a a) (+ 1 a))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
26×	`add-cbrt-cube` `add-exp-log`
20×	`pow-prod-down`
14×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-r` `add-cube-cbrt`
6×	`distribute-rgt-in` `distribute-lft-in` `prod-diff`
4×	`expm1-log1p-u` `pow-plus` `associate-*r/` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`pow2` `sub-neg` `pow-sqr`
1×	`flip3-+` `flip3--` `flip-+` `fma-udef` `flip--` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

Slowest

51.0ms	(* (* b b) (- 1 (* 3 a)))
47.0ms	(* (* a a) (+ 1 a))
24.0ms	(* (* a a) (* b b))
0.0ms	(fma (* b b) (* b b) (fma (* (* a a) (* b b)) 2 (pow a 4)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(fma (* b b) (* b b) (fma (* (* a a) (* b b)) 2 (pow a 4)))
83.0ms	(* (* b b) (- 1 (* 3 a)))
69.0ms	(* (* a a) (+ 1 a))
55.0ms	(* (* a a) (* b b))

simplify2.5s

Counts: 116 → 116

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))))
7.8b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))))
0.7b	(* (* b b) (- 1 (* 3 a)))
0.7b	(* (* b b) (- 1 (* 3 a)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `pow1`
14×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `prod-diff` `add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `sqrt-div` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `associate-l` `*-commutative` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

Slowest

78.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))))
64.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))))
35.0ms	(* (* b b) (- 1 (* 3 a)))
24.0ms	(* (* b b) (- 1 (* 3 a)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

199.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))))
192.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))))
85.0ms	(* (* b b) (- 1 (* 3 a)))
84.0ms	(* (* b b) (- 1 (* 3 a)))

simplify2.6s

Counts: 116 → 116

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes354.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

3.9s

20483×

body

valid