Details

sample114.0ms

Algorithm

intervals

Results

90.0ms

650×

body

valid

simplify220.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

220.0ms

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.0b	(* 4 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b	(+ (* a a) (* b b))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`fma-def` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
8×	`add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

Slowest

78.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
23.0ms	(pow (+ (* a a) (* b b)) 2)
20.0ms	(* 4 (* b b))
17.0ms	(+ (* a a) (* b b))

series195.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
64.0ms	(pow (+ (* a a) (* b b)) 2)
32.0ms	(+ (* a a) (* b b))
31.0ms	(* 4 (* b b))

simplify4.2s

Counts

38 → 92

Calls

38 calls:

Slowest

322.0ms	(* (* (* 4 4) 4) (* (* (* b b) (* b b)) (* b b)))
299.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
288.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
287.0ms	(+ (* 2 (* (pow a 2) (pow b 2))) (+ (* 4 (pow b 2)) (pow a 4)))
272.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a a) (* a a))
0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
0.0b	(* 2 (* a a))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
36×	`pow-prod-up`
27×	`pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`

Counts

4 → 122

Calls

4 calls:

Slowest

23.0ms	(* (* a a) (* a a))
13.0ms	(* 2 (* a a))
5.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

143.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
83.0ms	(* b (fma b b (* 2 (* a a))))
65.0ms	(* (* a a) (* a a))
42.0ms	(* 2 (* a a))

simplify5.6s

Counts

101 → 134

Calls

101 calls:

Slowest

989.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
419.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
375.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
346.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
321.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
0.0b	(* 2 (* a a))
0.0b	(* 4 (* b b))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
9×	`associate-l`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 78

Calls

4 calls:

Slowest

19.0ms	(* 2 (* a a))
18.0ms	(* b (fma b b (* 2 (* a a))))
13.0ms	(* 4 (* b b))
1.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series287.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
87.0ms	(* b (fma b b (* 2 (* a a))))
48.0ms	(* 4 (* b b))
44.0ms	(* 2 (* a a))

simplify4.5s

Counts

44 → 90

Calls

44 calls:

Slowest

874.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
722.0ms	(+ (pow b 3) (* 2 (* (pow a 2) b)))
303.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
294.0ms	(+ (pow b 3) (* 2 (* (pow a 2) b)))
292.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

9.9b	(cbrt (fma b b (* 2 (* a a))))
9.9b	(cbrt (fma b b (* 2 (* a a))))
9.9b	(cbrt (fma b b (* 2 (* a a))))
0.4b	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

7.0ms	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

197.0ms	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))
186.0ms	(cbrt (fma b b (* 2 (* a a))))
169.0ms	(cbrt (fma b b (* 2 (* a a))))
128.0ms	(cbrt (fma b b (* 2 (* a a))))

simplify3.0s

Counts

65 → 97

Calls

65 calls:

Slowest

263.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))
233.0ms	(* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a))))
231.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))
230.0ms	(* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a))))
206.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes548.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch5.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.0s

20764×

body

valid