Details

sample74.0ms

Algorithm

intervals

Results

62.0ms

617×

body

valid

simplify197.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

197.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))

rewrite143.0ms

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

96.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
26.0ms	(* 4 (* b b))
12.0ms	(+ (* a a) (* b b))
9.0ms	(pow (+ (* a a) (* b b)) 2)

series219.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
46.0ms	(pow (+ (* a a) (* b b)) 2)
44.0ms	(+ (* a a) (* b b))
28.0ms	(* 4 (* b b))

simplify3.9s

Counts

38 → 92

Calls

38 calls:

Slowest

311.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
305.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
282.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
275.0ms	(+ (* 2 (* (pow a 2) (pow b 2))) (+ (* 4 (pow b 2)) (pow a 4)))
270.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune944.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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))

rewrite74.0ms

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

28.0ms	(* 2 (* a a))
24.0ms	(* (* a a) (* a a))
10.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

107.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
94.0ms	(* b (fma b b (* 2 (* a a))))
63.0ms	(* (* a a) (* a a))
38.0ms	(* 2 (* a a))

simplify5.7s

Counts

101 → 134

Calls

101 calls:

Slowest

1.3s	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
349.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
347.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
336.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
314.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) a) (* (* a a) a)))

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

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))

rewrite43.0ms

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

17.0ms	(* 2 (* a a))
13.0ms	(* 4 (* b b))
11.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series316.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
86.0ms	(* b (fma b b (* 2 (* a a))))
48.0ms	(* 2 (* a a))
47.0ms	(* 4 (* b b))

simplify4.1s

Counts

44 → 90

Calls

44 calls:

Slowest

915.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
309.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
307.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
283.0ms	(* (* (* 4 4) 4) (* (* (* b b) (* b b)) (* b b)))
269.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)
0.5b	(* (cbrt b) (cbrt b))

rewrite21.0ms

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

15.0ms	(* (cbrt b) (cbrt b))
2.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

312.0ms	(* (cbrt b) (cbrt b))
286.0ms	(cbrt b)
279.0ms	(cbrt b)
266.0ms	(cbrt b)

simplify863.0ms

Counts

63 → 97

Calls

63 calls:

Slowest

143.0ms	(* (cbrt -1) (pow (* b -1) 1/3))
121.0ms	(* (cbrt -1) (pow (* b -1) 1/3))
96.0ms	(* (pow (cbrt -1) 2) (pow (pow b 2) 1/3))
95.0ms	(* (cbrt -1) (pow (* b -1) 1/3))
82.0ms	(* (* (cbrt (cbrt b)) (cbrt (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

3.1s

20417×

body

valid