Details

sample39.0ms

Algorithm

intervals

Results

24.0ms

657×

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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

rewrite50.0ms

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))
40.0ms	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
3.0ms	(+ (* a a) (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series253.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
50.0ms	(- (pow (+ (* a a) (* b b)) 2.0) 1.0)
29.0ms	(+ (* a a) (* b b))
101.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

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

prune237.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 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	(pow (hypot a b) (* 2 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

10.0ms	(- (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)))
1.0ms	(pow (hypot a b) (* 2 2.0))

series302.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(- (pow (hypot a b) (* 2 2.0)) 1.0)
106.0ms	(fma (* 4.0 b) b (+ (- (pow (hypot a b) (* 2 2.0)) 1.0) (fma (- 1.0) 1 1.0)))
122.0ms	(pow (hypot a b) (* 2 2.0))

simplify162.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	275	737
1	956	554
2	4922	523
3	5001	523

prune221.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (pow (sqrt (hypot a b)) (* 2 (* 2 2.0))) 1.0)
0.0b	(fma (* 4.0 b) b (+ (+ (- (pow (sqrt (hypot a b)) (* 2 (* 2 2.0))) 1.0) (- 1.0 1.0)) (fma (- 1.0) 1 1.0)))
0.9b	(pow (sqrt (hypot a b)) (* 2 (* 2 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`unpow-prod-down`
30×	`prod-diff`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
16×	`sqrt-prod`
10×	`fma-neg`
6×	`sqr-pow`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `difference-of-squares`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `pow-exp` `sqrt-pow2` `flip--` `fma-udef` `distribute-lft-out--`

Counts

3 → 92

Calls

3 calls:

22.0ms	(- (pow (sqrt (hypot a b)) (* 2 (* 2 2.0))) 1.0)
0.0ms	(fma (* 4.0 b) b (+ (+ (- (pow (sqrt (hypot a b)) (* 2 (* 2 2.0))) 1.0) (- 1.0 1.0)) (fma (- 1.0) 1 1.0)))
2.0ms	(pow (sqrt (hypot a b)) (* 2 (* 2 2.0)))

series392.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- (pow (sqrt (hypot a b)) (* 2 (* 2 2.0))) 1.0)
112.0ms	(fma (* 4.0 b) b (+ (+ (- (pow (sqrt (hypot a b)) (* 2 (* 2 2.0))) 1.0) (- 1.0 1.0)) (fma (- 1.0) 1 1.0)))
202.0ms	(pow (sqrt (hypot a b)) (* 2 (* 2 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	371	1231
1	1351	852
2	5002	757

prune280.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 b) b (+ (/ (fma (- 1.0) 1.0 (pow (hypot a b) (* 2 (* 2 2.0)))) (+ (pow (hypot a b) (* 2 2.0)) 1.0)) (fma (- 1.0) 1 1.0)))
0.0b	(pow (hypot a b) (* 2 (* 2 2.0)))
0.0b	(pow (hypot a b) (* 2 2.0))
10.5b	(/ (fma (- 1.0) 1.0 (pow (hypot a b) (* 2 (* 2 2.0)))) (+ (pow (hypot a b) (* 2 2.0)) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`add-exp-log`
6×	`pow1` `unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-unpow` `hypot-udef` `pow-pow` `pow-exp` `associate-/r/` `sqrt-pow2` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma (* 4.0 b) b (+ (/ (fma (- 1.0) 1.0 (pow (hypot a b) (* 2 (* 2 2.0)))) (+ (pow (hypot a b) (* 2 2.0)) 1.0)) (fma (- 1.0) 1 1.0)))
1.0ms	(pow (hypot a b) (* 2 (* 2 2.0)))
1.0ms	(pow (hypot a b) (* 2 2.0))
11.0ms	(/ (fma (- 1.0) 1.0 (pow (hypot a b) (* 2 (* 2 2.0)))) (+ (pow (hypot a b) (* 2 2.0)) 1.0))

series808.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(fma (* 4.0 b) b (+ (/ (fma (- 1.0) 1.0 (pow (hypot a b) (* 2 (* 2 2.0)))) (+ (pow (hypot a b) (* 2 2.0)) 1.0)) (fma (- 1.0) 1 1.0)))
123.0ms	(pow (hypot a b) (* 2 (* 2 2.0)))
127.0ms	(pow (hypot a b) (* 2 2.0))
400.0ms	(/ (fma (- 1.0) 1.0 (pow (hypot a b) (* 2 (* 2 2.0)))) (+ (pow (hypot a b) (* 2 2.0)) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	309	1038
1	1259	940
2	5001	914

prune357.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes67.0ms

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

sample1.1s

Algorithm

intervals

Results

736.0ms

20396×

body

valid