Details

sample177.0ms

Algorithm

intervals

Results

146.0ms

630×

body

valid

simplify186.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

185.0ms

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

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)

rewrite1.0ms

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

0.0ms	(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)

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

115.0ms	(fma (* a a) a (* a a))
107.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
64.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))
49.0ms	(fma -3 a 1)

simplify7.8s

Counts

56 → 56

Calls

56 calls:

Slowest

665.0ms	(* (* (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))
440.0ms	(* (* (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))))
375.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
346.0ms	(exp (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))))
319.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune844.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

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)))))

rewrite211.0ms

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

120.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
48.0ms	(* (* b b) (- 1 (* 3 a)))
24.0ms	(* (* a a) (+ 1 a))
16.0ms	(pow (+ (* a a) (* b b)) 2)

series294.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

88.0ms	(* (* b b) (- 1 (* 3 a)))
79.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
69.0ms	(pow (+ (* a a) (* b b)) 2)
58.0ms	(* (* a a) (+ 1 a))

simplify28.1s

Counts

140 → 123

Calls

140 calls:

Slowest

1.1s	(* (* (* (* a a) (+ 1 a)) (* (* a a) (+ 1 a))) (* (* a a) (+ 1 a)))
745.0ms	(* (sqrt 4) (sqrt (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
639.0ms	(* (sqrt 4) (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
499.0ms	(* (* (* 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))))))
471.0ms	(* 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)))))))

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize56.0ms

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)))

rewrite26.0ms

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

23.0ms	(* (* 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)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(cbrt (fma b b (* a a)))
113.0ms	(cbrt (fma b b (* a a)))
111.0ms	(cbrt (fma b b (* a a)))
70.0ms	(* (* b b) (- 1 (* 3 a)))

simplify10.2s

Counts

104 → 88

Calls

104 calls:

Slowest

374.0ms	(log1p (* (* b b) (- 1 (* 3 a))))
371.0ms	(log (* (* b b) (- 1 (* 3 a))))
363.0ms	(* (* b b) (fma (sqrt 1) (sqrt 1) (- (* a 3))))
362.0ms	(* (* b b) (- (pow 1 3) (pow (* 3 a) 3)))
341.0ms	(real->posit16 (* (* b b) (- 1 (* 3 a))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize77.0ms

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)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

168.0ms	(cbrt (fma b b (* a a)))
152.0ms	(cbrt (fma b b (* a a)))
148.0ms	(cbrt (fma b b (* a a)))
147.0ms	(cbrt (fma b b (* a a)))

simplify2.2s

Counts

76 → 68

Calls

76 calls:

Slowest

209.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
200.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
183.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
174.0ms	(+ (pow a 2/3) (* 1/3 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
86.0ms	(* (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) (cbrt (fma b b (* a a))))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes453.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample5.7s

Algorithm

intervals

Results

5.3s

20659×

body

valid