Details

sample37.0ms

Algorithm

intervals

Results

20.0ms

504×

body

valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	24	7
1	44	6
2	58	6
3	60	6
4	60	6

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 20.7b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
24.0b	(/ (* x x) (* y y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
225×	`times-frac`
162×	`add-cube-cbrt` `*-un-lft-identity`
96×	`swap-sqr` `associate-r` `associate-l`
32×	`*-commutative` `unswap-sqr`
15×	`associate-/r` `associate-/l`
14×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv`

Counts

2 → 285

Calls

2 calls:

1.0ms	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
16.0ms	(/ (* x x) (* y y))

series380.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
269.0ms	(/ (* x x) (* y y))

simplify62.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	928	1921
1	5001	1743

prune330.0ms

Filtered

291 candidates to 124 candidates (57.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	279	12	291
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	280	13	293

Merged error: 0.1b

Counts

293 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (/ z t) (/ x y))
0.0b	(hypot (/ z t) (/ x y))
0.5b	(* (hypot (/ z t) (/ x y)) (hypot (/ z t) (/ x y)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`hypot-udef`
5×	`add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `pow-prod-down` `prod-exp` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

1.0ms	(hypot (/ z t) (/ x y))
1.0ms	(hypot (/ z t) (/ x y))
4.0ms	(* (hypot (/ z t) (/ x y)) (hypot (/ z t) (/ x y)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(hypot (/ z t) (/ x y))
91.0ms	(hypot (/ z t) (/ x y))
139.0ms	(* (hypot (/ z t) (/ x y)) (hypot (/ z t) (/ x y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	104	364
1	351	302
2	1551	276
3	5001	271

prune128.0ms

Filtered

58 candidates to 44 candidates (24.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	51	7	58
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	57	14	71

Merged error: 0.0b

Counts

71 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (hypot (/ z t) (/ x y)) (* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y)))))
0.6b	(* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y))))
1.6b	(sqrt (hypot (/ z t) (/ x y)))
1.6b	(sqrt (hypot (/ z t) (/ x y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
50×	`sqrt-prod`
41×	`associate-r`
38×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`unswap-sqr`
22×	`swap-sqr`
16×	`sqrt-pow1` `pow1/2`
15×	`associate-l` `pow-prod-up`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow-prod-down`
5×	`pow-sqr` `*-commutative`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`rem-sqrt-square`
1×	`pow2` `hypot-udef` `pow-plus` `rem-square-sqrt`

Counts

4 → 149

Calls

4 calls:

19.0ms	(* (hypot (/ z t) (/ x y)) (* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y)))))
6.0ms	(* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y))))
1.0ms	(sqrt (hypot (/ z t) (/ x y)))
2.0ms	(sqrt (hypot (/ z t) (/ x y)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (hypot (/ z t) (/ x y)) (* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y)))))
92.0ms	(* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y))))
83.0ms	(sqrt (hypot (/ z t) (/ x y)))
89.0ms	(sqrt (hypot (/ z t) (/ x y)))

simplify73.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	260	1096
1	1173	898
2	5001	869

prune225.0ms

Filtered

161 candidates to 79 candidates (50.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	161	14	175

Merged error: 0.0b

Counts

175 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (hypot (/ z t) (/ x y)))) (sqrt (hypot (/ z t) (/ x y))))
1.6b	(sqrt (hypot (/ z t) (/ x y)))
1.6b	(sqrt (hypot (/ z t) (/ x y)))
1.6b	(sqrt (hypot (/ z t) (/ x y)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

31×	`sqrt-prod`
29×	`add-sqr-sqrt`
19×	`pow1`
15×	`sqrt-pow1`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1/2`
9×	`associate-l`
6×	`add-exp-log` `associate-r` `pow-prod-up` `add-cbrt-cube` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow-prod-down`
2×	`pow-plus` `cube-unmult`
1×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

8.0ms	(* (sqrt (sqrt (hypot (/ z t) (/ x y)))) (sqrt (hypot (/ z t) (/ x y))))
1.0ms	(sqrt (hypot (/ z t) (/ x y)))
1.0ms	(sqrt (hypot (/ z t) (/ x y)))
2.0ms	(sqrt (hypot (/ z t) (/ x y)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (sqrt (sqrt (hypot (/ z t) (/ x y)))) (sqrt (hypot (/ z t) (/ x y))))
87.0ms	(sqrt (hypot (/ z t) (/ x y)))
88.0ms	(sqrt (hypot (/ z t) (/ x y)))
89.0ms	(sqrt (hypot (/ z t) (/ x y)))

simplify155.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	177	745
1	513	684
2	1271	639
3	4698	628
4	5001	628

prune211.0ms

Filtered

104 candidates to 71 candidates (31.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	104	14	118

Merged error: 0b

Counts

118 → 14

regimes414.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	14
1	15	14

end0.0ms

sample921.0ms

Algorithm

intervals

Results

544.0ms

15412×

body

valid