Details

sample154.0ms

Algorithm

intervals

Results

129.0ms

630×

body

valid

simplify197.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

197.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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

4 → 44

Calls

4 calls:

Slowest

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

series344.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(fma (* a a) a (* a a))
93.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
84.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))
45.0ms	(fma -3 a 1)

simplify8.0s

Counts

56 → 56

Calls

56 calls:

Slowest

603.0ms	(sqrt (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))))
435.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
421.0ms	(* (* (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))) (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))))
369.0ms	(* (* (fma -3 a 1) (fma -3 a 1)) (fma -3 a 1))
347.0ms	(* (* (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))

prune891.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

Slowest

100.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
35.0ms	(* (* b b) (- 1 (* 3 a)))
29.0ms	(* (* a a) (+ 1 a))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series241.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
65.0ms	(* (* b b) (- 1 (* 3 a)))
54.0ms	(pow (+ (* a a) (* b b)) 2)
50.0ms	(* (* a a) (+ 1 a))

simplify26.9s

Counts

140 → 123

Calls

140 calls:

Slowest

956.0ms	(* (* (* (* a a) (+ 1 a)) (* (* a a) (+ 1 a))) (* (* a a) (+ 1 a)))
690.0ms	(* (sqrt 4) (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
639.0ms	(real->posit16 (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
505.0ms	(* 4 (+ (* (* (* a a) (+ (pow 1 3) (pow a 3))) (+ 1 (* 3 a))) (* (+ (* 1 1) (- (* a a) (* 1 a))) (* (* b b) (- (* 1 1) (* (* 3 a) (* 3 a)))))))
449.0ms	(* (* (* 4 4) 4) (* (* (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))) (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))) (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
0.7b	(* (* b b) (- 1 (* 3 a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

Slowest

27.0ms	(* (* b b) (- 1 (* 3 a)))
1.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))
1.0ms	(cbrt (fma b b (* a a)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(cbrt (fma b b (* a a)))
135.0ms	(cbrt (fma b b (* a a)))
133.0ms	(cbrt (fma b b (* a a)))
59.0ms	(* (* b b) (- 1 (* 3 a)))

simplify10.4s

Counts

104 → 88

Calls

104 calls:

Slowest

421.0ms	(* (* b b) (- (pow 1 3) (pow (* 3 a) 3)))
344.0ms	(* (* b b) (fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* a 3))))
343.0ms	(log (* (* b b) (- 1 (* 3 a))))
340.0ms	(expm1 (* (* b b) (- 1 (* 3 a))))
328.0ms	(sqrt (* (* b b) (- 1 (* 3 a))))

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))
10.4b	(cbrt (fma b b (* a a)))

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

series568.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(cbrt (fma b b (* a a)))
142.0ms	(cbrt (fma b b (* a a)))
131.0ms	(cbrt (fma b b (* a a)))
130.0ms	(cbrt (fma b b (* a a)))

simplify2.2s

Counts

76 → 68

Calls

76 calls:

Slowest

186.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
185.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
173.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
171.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
85.0ms	(* (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) (cbrt (fma b b (* a a))))

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes487.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

5.1s

20659×

body

valid