Details

sample58.0ms

Algorithm

intervals

Results

35.0ms

713×

body

valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	53	14
1	173	13
2	532	12
3	1681	12
4	4278	12
5	5001	12

prune6.0ms

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)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.8b	(* (* b b) (+ 3.0 a))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
7×	`fma-def`
6×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

60.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
34.0ms	(* (* a a) (- 1.0 a))
9.0ms	(pow (+ (* a a) (* b b)) 2.0)
29.0ms	(* (* b b) (+ 3.0 a))

series274.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
51.0ms	(* (* a a) (- 1.0 a))
95.0ms	(pow (+ (* a a) (* b b)) 2.0)
29.0ms	(* (* b b) (+ 3.0 a))

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	646	990
1	3454	779
2	5001	776

prune326.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.2b	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.8b	(* (* b b) (+ 3.0 a))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`associate-*r/` `prod-diff`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

81.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
35.0ms	(* (* a a) (- 1.0 a))
0.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
29.0ms	(* (* b b) (+ 3.0 a))

series241.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
45.0ms	(* (* a a) (- 1.0 a))
105.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
33.0ms	(* (* b b) (+ 3.0 a))

simplify113.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	729	1176
1	4233	935
2	5001	935

prune349.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (+ 3.0 a))
0.8b	(* (* b b) (+ 3.0 a))
11.8b	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.8b	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-r`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

31.0ms	(* (* b b) (+ 3.0 a))
29.0ms	(* (* b b) (+ 3.0 a))
1.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
2.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* b b) (+ 3.0 a))
29.0ms	(* (* b b) (+ 3.0 a))
216.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
211.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	298	1002
1	1289	910
2	5002	902

prune377.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (+ 3.0 a))
11.8b	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.8b	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.8b	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
8×	`add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-l` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

32.0ms	(* (* b b) (+ 3.0 a))
1.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
1.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
2.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* b b) (+ 3.0 a))
223.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
213.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
213.0ms	(sqrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	298	1239
1	1289	1143
2	5002	1131

prune355.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes135.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	76
1	41	76

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

20279×

body

valid