Details

sample107.0ms

Algorithm

intervals

Results

84.0ms

710×

body

valid

simplify239.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

239.0ms

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
0.0b	(fma a a (* b b))
0.0b	(fma a a (* b b))
0.0b	(fma (* b b) 4 -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 a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
0.0ms	(fma a a (* b b))
0.0ms	(fma a a (* b b))
0.0ms	(fma (* b b) 4 -1)

series295.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
68.0ms	(fma (* b b) 4 -1)
55.0ms	(fma a a (* b b))
49.0ms	(fma a a (* b b))

simplify992.0ms

Counts

12 → 56

Calls

12 calls:

Slowest

333.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
318.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
122.0ms	(- (+ (pow a 4) (* 4 (pow b 2))) 1)
42.0ms	(- (* 4 (pow b 2)) 1)
39.0ms	(- (* 4 (pow b 2)) 1)

prune683.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

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))

rewrite125.0ms

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

88.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
14.0ms	(* 4 (* b b))
14.0ms	(pow (+ (* a a) (* b b)) 2)
8.0ms	(+ (* a a) (* b b))

series196.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
39.0ms	(+ (* a a) (* b b))
38.0ms	(pow (+ (* a a) (* b b)) 2)
32.0ms	(* 4 (* b b))

simplify4.6s

Counts

38 → 92

Calls

38 calls:

Slowest

619.0ms	(* (exp (* a a)) (exp (* b b)))
327.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
313.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
300.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
299.0ms	(+ (* 2 (* (pow a 2) (pow b 2))) (+ (* 4 (pow b 2)) (pow a 4)))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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

48.0ms	(* (* a a) (* a a))
24.0ms	(* 4 (* b b))
12.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
86.0ms	(* b (fma b b (* 2 (* a a))))
49.0ms	(* 4 (* b b))
41.0ms	(* (* a a) (* a a))

simplify5.1s

Counts

101 → 134

Calls

101 calls:

Slowest

835.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
403.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
370.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
305.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
304.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

Slowest

15.0ms	(* 4 (* b b))
7.0ms	(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (* b b)))
6.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series366.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (* b b)))
111.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
76.0ms	(* b (fma b b (* 2 (* a a))))
51.0ms	(* 4 (* b b))

simplify5.3s

Counts

38 → 86

Calls

38 calls:

Slowest

819.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
418.0ms	(sqrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
368.0ms	(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))
319.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
317.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes330.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.2s

20415×

body

valid