Details

sample53.0ms

Algorithm

intervals

Results

33.0ms

679×

body

valid

simplify52.0ms

Algorithm

egg-herbie

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite21.0ms

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:

4.0ms	(+ (* a a) (* b b))
9.0ms	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
1.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series266.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a a) (* b b))
55.0ms	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
76.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
106.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

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

prune225.0ms

Filtered

101 candidates to 71 candidates (70.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Merged error: 0b

Counts

102 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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:

7.0ms	(- (pow (hypot a b) (* 2 2.0)) 1.0)
1.0ms	(hypot a b)
1.0ms	(fma (* 4.0 b) b (+ (- (pow (hypot a b) (* 2 2.0)) 1.0) (fma (- 1.0) 1 1.0)))
2.0ms	(pow (hypot a b) (* 2 2.0))

series370.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (pow (hypot a b) (* 2 2.0)) 1.0)
47.0ms	(hypot a b)
116.0ms	(fma (* 4.0 b) b (+ (- (pow (hypot a b) (* 2 2.0)) 1.0) (fma (- 1.0) 1 1.0)))
129.0ms	(pow (hypot a b) (* 2 2.0))

simplify165.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (33.0ms)

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

prune248.0ms

Filtered

96 candidates to 70 candidates (72.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Merged error: 0b

Counts

99 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
2.1b	(expm1 (log1p (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))))
2.3b	(log1p (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `expm1-log1p-u`
4×	`add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
1×	`pow-to-exp` `log1p-udef` `expm1-log1p` `pow-pow` `log1p-expm1` `pow-exp` `fma-udef` `expm1-udef` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

1.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
1.0ms	(expm1 (log1p (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))))
1.0ms	(log1p (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
108.0ms	(pow (+ (* a a) (* b b)) 2.0)
167.0ms	(expm1 (log1p (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))))
133.0ms	(log1p (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	228	513
1	765	451
2	3012	435
3	5002	432

prune185.0ms

Filtered

63 candidates to 55 candidates (87.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	63	3	66

Merged error: 0b

Counts

66 → 3

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

20618×

body

valid