Details

sample52.0ms

Algorithm

intervals

Results

31.0ms

669×

body

valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	8
1	41	8
2	67	8
3	119	8
4	309	8
5	1494	8
6	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
3×	`unpow-prod-down` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr` `sqr-pow`

Counts

4 → 58

Calls

4 calls:

9.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms	(+ (* a a) (* b b))
5.0ms	(* 4.0 (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series60.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
9.0ms	(+ (* a a) (* b b))
5.0ms	(* 4.0 (* b b))
28.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	366	432
1	1534	398
2	5001	390

prune99.0ms

Filtered

70 candidates to 49 candidates (30.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0.0b

Counts

71 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
3.9b	(* (pow a 2) (pow b 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
28×	`prod-exp`
25×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`-un-lft-identity` `associate-l*` `add-cbrt-cube` `add-log-exp`
10×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `associate-r`
6×	`pow1`
4×	`sum-log` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

7.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
4.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

series36.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
9.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
9.0ms	(* 2 (* (pow a 2) (pow b 2)))
6.0ms	(* (pow a 2) (pow b 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	375	699
1	1613	621
2	5001	616

prune165.0ms

Filtered

113 candidates to 60 candidates (46.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Merged error: 0.0b

Counts

117 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.1b	(* (neg (pow b 3)) b)
0.3b	(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
21.4b	(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
24×	`unpow-prod-down` `times-frac`
16×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`difference-of-squares`
6×	`cube-prod`
4×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`pow-unpow` `associate-/l*` `sqr-pow`
2×	`cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `*-commutative` `flip--` `div-inv` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `distribute-lft-neg-out` `pow-to-exp` `neg-mul-1` `pow-pow` `frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 131

Calls

4 calls:

5.0ms	(* 4.0 (* b b))
8.0ms	(* (neg (pow b 3)) b)
12.0ms	(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
12.0ms	(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 4.0 (* b b))
4.0ms	(* (neg (pow b 3)) b)
27.0ms	(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
13.0ms	(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

simplify107.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	624	1336
1	3292	1227
2	5002	1223

prune279.0ms

Filtered

143 candidates to 107 candidates (25.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	143	4	147

Merged error: 0b

Counts

147 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b)) 2.0)
0.4b	(pow (/ 1 (+ a b)) 2.0)
3.0b	(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b))
23.6b	(* (pow (/ 1 (+ a b)) 2.0) (pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b)) 2.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
100×	`unpow-prod-down`
88×	`*-un-lft-identity`
82×	`times-frac`
62×	`add-exp-log`
52×	`add-cube-cbrt`
34×	`pow-exp`
25×	`associate-r`
24×	`prod-exp`
22×	`associate-l`
20×	`unswap-sqr`
18×	`div-exp`
13×	`sqr-pow`
12×	`pow-to-exp`
10×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`pow-unpow` `distribute-lft-out`
5×	`rec-exp` `1-exp` `associate-/r*` `div-inv`
4×	`pow-pow` `add-log-exp`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 213

Calls

4 calls:

21.0ms	(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b)) 2.0)
12.0ms	(pow (/ 1 (+ a b)) 2.0)
19.0ms	(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b))
31.0ms	(* (pow (/ 1 (+ a b)) 2.0) (pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b)) 2.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b)) 2.0)
27.0ms	(pow (/ 1 (+ a b)) 2.0)
9.0ms	(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b))
156.0ms	(* (pow (/ 1 (+ a b)) 2.0) (pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- a b)) 2.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1008	3107
1	4010	2990
2	5001	2972

prune562.0ms

Filtered

225 candidates to 149 candidates (33.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	225	4	229

Merged error: 0b

Counts

229 → 4

regimes250.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

932.0ms

20269×

body

valid

Details

sample52.0ms

simplify57.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series60.0ms

simplify41.0ms

prune99.0ms

localize13.0ms

rewrite28.0ms

series36.0ms

simplify69.0ms

prune165.0ms

localize17.0ms

rewrite43.0ms

series46.0ms

simplify107.0ms

prune279.0ms

localize22.0ms

rewrite101.0ms

series228.0ms

simplify115.0ms

prune562.0ms

regimes250.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

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