Details

sample49.0ms

Algorithm

intervals

Results

28.0ms

709×

body

valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7
done	5002	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0b	(+ (* a a) (* b b))
0.0b	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt` `prod-diff`
16×	`unpow-prod-down`
8×	`add-log-exp`
7×	`fma-neg`
6×	`sqr-pow`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `fma-def` `flip3-+` `diff-log` `pow-exp` `sum-log` `flip--` `flip-+` `fma-udef` `distribute-lft-out--`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
8.0ms	(+ (* a a) (* b b))
88.0ms	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series269.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
33.0ms	(+ (* a a) (* b b))
52.0ms	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
106.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify45.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	362	897
1	1404	668
2	5002	656
done	5002	656

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (pow (hypot a b) (* 2 2.0)) 1.0)
0.0b	(fma (* 4.0 b) b (+ (- (pow (hypot a b) (* 2 2.0)) 1.0) (fma (- 1.0) 1 1.0)))
0.0b	(hypot a b)
0.0b	(pow (hypot a b) (* 2 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`prod-diff`
20×	`add-cube-cbrt`
16×	`unpow-prod-down`
7×	`fma-neg`
6×	`add-log-exp` `sqr-pow`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`hypot-udef`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `pow-pow` `diff-log` `pow-exp` `sqrt-pow2` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

23.0ms	(- (pow (hypot a b) (* 2 2.0)) 1.0)
0.0ms	(fma (* 4.0 b) b (+ (- (pow (hypot a b) (* 2 2.0)) 1.0) (fma (- 1.0) 1 1.0)))
0.0ms	(hypot a b)
6.0ms	(pow (hypot a b) (* 2 2.0))

series371.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (pow (hypot a b) (* 2 2.0)) 1.0)
120.0ms	(fma (* 4.0 b) b (+ (- (pow (hypot a b) (* 2 2.0)) 1.0) (fma (- 1.0) 1 1.0)))
51.0ms	(hypot a b)
124.0ms	(pow (hypot a b) (* 2 2.0))

simplify160.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	287	763
1	982	578
2	4979	547
3	5001	547
done	5001	547

prune270.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (hypot a b) (* 2 2.0))) (cbrt (pow (hypot a b) (* 2 2.0))))
17.5b	(cbrt (pow (hypot a b) (* 2 2.0)))
17.5b	(cbrt (pow (hypot a b) (* 2 2.0)))
17.5b	(cbrt (pow (hypot a b) (* 2 2.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

30.0ms	(* (cbrt (pow (hypot a b) (* 2 2.0))) (cbrt (pow (hypot a b) (* 2 2.0))))
3.0ms	(cbrt (pow (hypot a b) (* 2 2.0)))
3.0ms	(cbrt (pow (hypot a b) (* 2 2.0)))
3.0ms	(cbrt (pow (hypot a b) (* 2 2.0)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (cbrt (pow (hypot a b) (* 2 2.0))) (cbrt (pow (hypot a b) (* 2 2.0))))
175.0ms	(cbrt (pow (hypot a b) (* 2 2.0)))
169.0ms	(cbrt (pow (hypot a b) (* 2 2.0)))
175.0ms	(cbrt (pow (hypot a b) (* 2 2.0)))

simplify103.0ms

Counts

129 → 129

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	216	1307
1	719	1239
2	3438	1170
3	5001	1164
done	5001	1164

prune479.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 4.0 b) b (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
0.0b	(* 2 (pow a 2))
1.2b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (* 4.0 b) b (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
16.0ms	(* 2 (pow a 2))
0.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series173.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma (* 4.0 b) b (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
30.0ms	(* 2 (pow a 2))
70.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify143.0ms

Counts

58 → 58

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	176	342
1	715	298
2	3609	296
3	5001	289
done	5001	289

prune171.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9
done	21	9

end0.0ms

sample1.2s

Algorithm

intervals

Results

761.0ms

20533×

body

valid