Details

sample32.0ms

Algorithm

intervals

Results

16.0ms

438×

body

valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	55	7
2	101	7
3	182	7
4	335	7
5	731	7
6	1828	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
6.1b	(- (+ (* x x) (* y y)) (* z z))
25.6b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`times-frac` `associate-/l*`
3×	`pow1` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `sum-log` `flip--` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 52

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
40.0ms	(- (+ (* x x) (* y y)) (* z z))
72.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series135.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (* x x) (* y y))
37.0ms	(- (+ (* x x) (* y y)) (* z z))
73.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	520
1	1492	454
2	5001	446

prune149.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
0.2b	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
8.6b	(/ (pow x 2) y)
10.7b	(/ (pow z 2) y)

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
56×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
26×	`unpow-prod-down`
16×	`add-exp-log` `associate-/l*`
10×	`associate-r` `add-cbrt-cube` `unpow2` `difference-of-squares` `sqr-pow`
9×	`add-log-exp`
6×	`pow1` `div-exp` `associate-/r*`
4×	`associate-*r/` `frac-sub` `distribute-lft-out--`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `associate--l+`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

163.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
332.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
8.0ms	(/ (pow x 2) y)
11.0ms	(/ (pow z 2) y)

series127.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
51.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
22.0ms	(/ (pow x 2) y)
18.0ms	(/ (pow z 2) y)

simplify72.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	523	1126
1	2010	1020
2	5001	1014

prune373.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
0.2b	(* z (/ z y))
0.2b	(* 0.5 (- (+ y (/ (pow x 2) y)) (* z (/ z y))))
8.6b	(/ (pow x 2) y)

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
34×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `associate-r`
13×	`add-cbrt-cube`
12×	`unpow-prod-down`
9×	`associate-*r/` `add-log-exp`
8×	`pow1` `associate-/l*`
6×	`associate-l`
4×	`div-exp` `frac-sub` `unpow2` `sqr-pow`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-exp` `associate--l+` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip--` `flip-+` `div-inv`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log`

Counts

4 → 125

Calls

4 calls:

149.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
13.0ms	(* z (/ z y))
280.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (* z (/ z y))))
9.0ms	(/ (pow x 2) y)

series128.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
17.0ms	(* z (/ z y))
49.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (* z (/ z y))))
21.0ms	(/ (pow x 2) y)

simplify64.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	502	881
1	2256	790
2	5001	787

prune286.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* x (/ x y))) (* z (/ z y)))
0.2b	(* x (/ x y))
0.2b	(* z (/ z y))
0.2b	(* 0.5 (- (+ y (* x (/ x y))) (* z (/ z y))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
16×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-*r/`
9×	`associate-l` `add-log-exp`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`frac-sub`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `associate--l+` `*-commutative`
2×	`cbrt-undiv` `flip3--` `flip3-+` `diff-log` `div-exp` `flip--` `flip-+` `div-inv`
1×	`sum-log`

Counts

4 → 108

Calls

4 calls:

27.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
14.0ms	(* x (/ x y))
13.0ms	(* z (/ z y))
60.0ms	(* 0.5 (- (+ y (* x (/ x y))) (* z (/ z y))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
18.0ms	(* x (/ x y))
17.0ms	(* z (/ z y))
50.0ms	(* 0.5 (- (+ y (* x (/ x y))) (* z (/ z y))))

simplify70.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	517	773
1	2589	691
2	5002	691

prune237.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes91.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample822.0ms

Algorithm

intervals

Results

432.0ms

13738×

body

valid