Details

sample53.0ms

Algorithm

intervals

Results

34.0ms

622×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
7×	`distribute-rgt-in` `fma-def` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `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`

Counts

4 → 100

Calls

4 calls:

27.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
17.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
66.0ms	(* (* a a) (+ 1.0 a))
131.0ms	(pow (+ (* a a) (* b b)) 2.0)
65.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify91.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	564	828
1	2826	724
2	5001	715

prune400.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))
8.2b	(sqrt (+ (* a a) (* b b)))
8.2b	(sqrt (+ (* a a) (* b b)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff` `sqrt-prod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `hypot-def`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `fma-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(sqrt (+ (* a a) (* b b)))
4.0ms	(sqrt (+ (* a a) (* b b)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
61.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
55.0ms	(sqrt (+ (* a a) (* b b)))
48.0ms	(sqrt (+ (* a a) (* b b)))

simplify57.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	379	738
1	1669	640
2	5001	616

prune385.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
0.0b	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`add-cube-cbrt` `associate-+r+` `associate-*r/` `prod-diff`
8×	`fma-def` `add-log-exp`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `frac-add` `log1p-expm1-u`
3×	`unpow-prod-down` `flip3--` `flip--`
2×	`+-commutative` `associate-+l+` `associate-l` `sum-log` `*-commutative` `unswap-sqr`
1×	`distribute-lft-out` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

12.0ms	(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
8.0ms	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms	(* (* a a) (+ 1.0 a))
17.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
154.0ms	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms	(* (* a a) (+ 1.0 a))
59.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify128.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	731	1066
1	3888	940
2	5001	925

prune467.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
0.1b	(* (* a a) (- (* 1.0 1.0) (* a a)))
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`pow1`
12×	`add-cube-cbrt`
9×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
8×	`prod-diff`
7×	`fma-def` `associate-r`
6×	`associate-*r/` `pow-prod-down` `add-log-exp`
5×	`times-frac` `associate-/r*`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `unpow-prod-down` `div-exp` `difference-of-squares`
2×	`associate-+r+` `associate-l` `associate-/r/` `*-commutative` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `div-inv` `associate-/l*` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

16.0ms	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
16.0ms	(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
15.0ms	(* (* a a) (- (* 1.0 1.0) (* a a)))
12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

398.0ms	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
126.0ms	(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
90.0ms	(* (* a a) (- (* 1.0 1.0) (* a a)))
61.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify117.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	708	1200
1	3809	1024
2	5002	1016

prune484.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	18
1	31	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20276×

body

valid