Details

sample114.0ms

Algorithm

intervals

Results

88.0ms

620×

body

valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4618
5	1889
4	575
3	160
2	62
1	29
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

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:

65.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
15.0ms	(+ (* a a) (* b b))
32.0ms	(* 4 (* b b))
9.0ms	(pow (+ (* a a) (* b b)) 2)

series221.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
33.0ms	(+ (* a a) (* b b))
44.0ms	(* 4 (* b b))
62.0ms	(pow (+ (* a a) (* b b)) 2)

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1586
1	384
0	121

prune404.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a a (* b b))
0.0b	(+ (* 1 (* (fma a a (* b b)) (fma a a (* b b)))) (* 4 (* b b)))
0.0b	(* 4 (* b b))
0.3b	(* (fma a a (* b b)) (fma a a (* b b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`fma-udef`
6×	`associate-l` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-+l+` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`swap-sqr`
2×	`*-commutative` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `fma-def` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 82

Calls

4 calls:

0.0ms	(fma a a (* b b))
29.0ms	(+ (* 1 (* (fma a a (* b b)) (fma a a (* b b)))) (* 4 (* b b)))
24.0ms	(* 4 (* b b))
10.0ms	(* (fma a a (* b b)) (fma a a (* b b)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma a a (* b b))
83.0ms	(+ (* 1 (* (fma a a (* b b)) (fma a a (* b b)))) (* 4 (* b b)))
45.0ms	(* 4 (* b b))
66.0ms	(* (fma a a (* b b)) (fma a a (* b b)))

simplify2.9s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	3639
2	1036
1	330
0	121

prune390.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
0.2b	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
11.0b	(sqrt (fma a a (* b b)))
11.0b	(sqrt (fma a a (* b b)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
19×	`add-sqr-sqrt`
15×	`pow-prod-up`
13×	`sqrt-prod`
12×	`sqrt-pow1` `pow1/2` `associate-l`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`fma-udef`
6×	`pow-plus`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `cube-unmult` `*-commutative` `hypot-def` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

15.0ms	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
37.0ms	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
2.0ms	(sqrt (fma a a (* b b)))
2.0ms	(sqrt (fma a a (* b b)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sqrt (fma a a (* b b))) (fma a a (* b b)))
47.0ms	(* (sqrt (fma a a (* b b))) (* (sqrt (fma a a (* b b))) (fma a a (* b b))))
50.0ms	(sqrt (fma a a (* b b)))
73.0ms	(sqrt (fma a a (* b b)))

simplify1.8s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
3	2188
2	737
1	275
0	108

prune593.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1 (pow (sqrt (fma a a (* b b))) 4)) (* 4 (* b b)))
0.0b	(* 4 (* b b))
0.1b	(pow (sqrt (fma a a (* b b))) 4)
11.0b	(sqrt (fma a a (* b b)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`unpow-prod-down` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `fma-def` `flip3-+` `associate-r` `pow-exp` `*-commutative` `flip-+` `fma-udef` `hypot-def` `sqrt-pow2` `unswap-sqr` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

12.0ms	(+ (* 1 (pow (sqrt (fma a a (* b b))) 4)) (* 4 (* b b)))
27.0ms	(* 4 (* b b))
5.0ms	(pow (sqrt (fma a a (* b b))) 4)
3.0ms	(sqrt (fma a a (* b b)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (* 1 (pow (sqrt (fma a a (* b b))) 4)) (* 4 (* b b)))
51.0ms	(* 4 (* b b))
81.0ms	(pow (sqrt (fma a a (* b b))) 4)
58.0ms	(sqrt (fma a a (* b b)))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1338
1	368
0	123

prune435.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes103.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	12

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.2s

20337×

body

valid