Details

sample29.0ms

Algorithm

intervals

Results

15.0ms

454×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 24.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (- (* y y) (* z z)))
2.2b	(- (* y y) (* z z))
22.8b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv` `add-log-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `flip--` `fma-udef` `associate-/l/` `difference-of-squares`

Counts

3 → 99

Calls

3 calls:

1.0ms	(fma x x (- (* y y) (* z z)))
4.0ms	(- (* y y) (* z z))
7.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series200.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma x x (- (* y y) (* z z)))
41.0ms	(- (* y y) (* z z))
104.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	466	1096
1	1881	1029
2	5001	1026

prune369.0ms

Filtered

108 candidates to 87 candidates (80.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 10.9b

Counts

109 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
9.5b	(/ (pow z 2) y)
9.9b	(/ (pow x 2) y)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
148×	`times-frac`
138×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
112×	`prod-diff`
61×	`unpow-prod-down`
30×	`distribute-lft-out`
21×	`unpow2` `sqr-pow`
16×	`associate-/l*`
13×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*` `div-inv`
5×	`difference-of-squares`
4×	`fma-neg`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `diff-log` `pow-exp` `clear-num` `frac-sub` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `flip3-+` `associate--l+` `sum-log` `flip--` `flip-+`

Counts

3 → 243

Calls

3 calls:

28.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
5.0ms	(/ (pow z 2) y)
6.0ms	(/ (pow x 2) y)

series92.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
19.0ms	(/ (pow z 2) y)
21.0ms	(/ (pow x 2) y)

simplify129.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	957	4380
1	3231	3066
2	5002	2871

prune468.0ms

Filtered

252 candidates to 103 candidates (40.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	6	2	8
Picked	1	0	1
Done	0	1	1
Total	254	8	262

Merged error: 0.8b

Counts

262 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
0.2b	(* (fabs x) (/ (fabs x) y))
9.5b	(/ (pow z 2) y)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-sqr-sqrt`
110×	`times-frac`
104×	`*-un-lft-identity`
102×	`add-cube-cbrt`
84×	`prod-diff`
40×	`unpow-prod-down`
14×	`unpow2` `sqr-pow`
13×	`add-exp-log` `associate-r`
10×	`add-cbrt-cube`
8×	`associate-/l*` `add-log-exp`
5×	`pow1` `div-inv` `difference-of-squares`
4×	`div-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-l` `associate-/r*` `log1p-expm1-u`
2×	`cbrt-undiv` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `sum-log` `-commutative` `flip--` `flip-+` `distribute-lft-out--`

Counts

3 → 196

Calls

3 calls:

16.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
7.0ms	(* (fabs x) (/ (fabs x) y))
5.0ms	(/ (pow z 2) y)

series100.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
20.0ms	(* (fabs x) (/ (fabs x) y))
24.0ms	(/ (pow z 2) y)

simplify139.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	990	3973
1	3642	2812
2	5001	2802

prune471.0ms

Filtered

205 candidates to 102 candidates (49.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	206	7	213

Merged error: 0.0b

Counts

213 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

644×	`times-frac`
446×	`add-sqr-sqrt`
422×	`*-un-lft-identity`
420×	`add-cube-cbrt`
288×	`prod-diff`
161×	`unpow-prod-down`
55×	`sqr-pow`
34×	`div-inv`
21×	`add-exp-log`
13×	`associate-r` `associate-/r*` `add-cbrt-cube`
10×	`div-exp`
8×	`add-log-exp`
7×	`associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r/`
3×	`expm1-log1p-u` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`pow-to-exp` `diff-log` `pow-exp` `prod-exp` `frac-sub` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip--` `flip-+` `distribute-lft-out--`

Counts

3 → 483

Calls

3 calls:

39.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z (/ 2 2)) (/ y z)))
13.0ms	(/ (pow z (/ 2 2)) (/ y z))
8.0ms	(* (fabs x) (/ (fabs x) y))

series112.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z (/ 2 2)) (/ y z)))
22.0ms	(/ (pow z (/ 2 2)) (/ y z))
24.0ms	(* (fabs x) (/ (fabs x) y))

simplify176.0ms

Algorithm

egg-herbie

Counts

492 → 492

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2701	14920
1	5002	11314

prune942.0ms

Filtered

492 candidates to 180 candidates (36.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	490	2	492
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	492	7	499

Merged error: 0.0b

Counts

499 → 7

regimes150.0ms

Accuracy

0% (0.1b 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	20	10
1	21	10
2	21	10

end0.0ms

sample763.0ms

Algorithm

intervals

Results

480.0ms

13692×

body

valid