Details

sample66.0ms

Algorithm

intervals

Results

51.0ms

654×

body

valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	4855
5	1985
4	584
3	159
2	60
1	27
0	12

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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)

rewrite131.0ms

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:

86.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
15.0ms	(+ (* a a) (* b b))
19.0ms	(* 4 (* b b))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series250.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
51.0ms	(+ (* a a) (* b b))
50.0ms	(* 4 (* b b))
55.0ms	(pow (+ (* a a) (* b b)) 2)

simplify4.1s

Counts

92 → 92

Iterations

Iter	Nodes
3	6000
2	1477
1	359
0	121

prune976.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (* a a) (* b b))
0.0b	(* 4 (* b b))
0.2b	(fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

9.0ms	(+ (* a a) (* b b))
7.0ms	(+ (* a a) (* b b))
17.0ms	(* 4 (* b b))
0.0ms	(fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* a a) (* b b))
35.0ms	(+ (* a a) (* b b))
39.0ms	(* 4 (* b b))
90.0ms	(fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))

simplify2.3s

Counts

75 → 75

Iterations

Iter	Nodes
3	4277
2	902
1	246
0	84

prune679.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))) (cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))))
13.4b	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
13.4b	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
13.4b	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b 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:

15.0ms	(* (cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))) (cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))))
1.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
1.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
2.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))

series898.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))) (cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b)))))
243.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
241.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
239.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
4	4736
3	1396
2	531
1	210
0	96

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

12.8b	(sqrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
12.8b	(sqrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
13.4b	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
13.4b	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

2.0ms	(sqrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
2.0ms	(sqrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
1.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
1.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))

series855.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
174.0ms	(sqrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
286.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))
248.0ms	(cbrt (fma (+ (* a a) (* b b)) (+ (* a a) (* b b)) (* 4 (* b b))))

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
4	3279
3	1072
2	363
1	151
0	75

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	10

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.1s

20707×

body

valid