Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	284×	body	80	valid
3.0ms	75×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	7

prune2.0ms

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: 23.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

1106×	`add-sqr-sqrt`
514×	`associate-l`
470×	`*-un-lft-identity`
440×	`times-frac`
408×	`sqrt-prod`
291×	`unswap-sqr`
270×	`add-cube-cbrt`
250×	`difference-of-squares`
216×	`associate-r`
180×	`prod-diff`
122×	`*-commutative`
100×	`distribute-lft-out--`
89×	`swap-sqr`
22×	`associate-/l*`
20×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`fma-neg`
10×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `div-inv`

Counts

4 → 789

Calls

4 calls:

20.0ms	(- (* z z) (* t a))
7.0ms	(* (* x y) z)
37.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.0ms	(sqrt (- (* z z) (* t a)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
24.0ms	(* (* x y) z)
83.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify142.0ms

Algorithm

egg-herbie

Counts

801 → 801

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	1728	10568
1	5001	9141

prune782.0ms

Filtered

801 candidates to 275 candidates (65.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	793	8	801
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	794	8	802

Merged error: 3.5b

Counts

802 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.4b	(- (* z z) (* t a))
2.7b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

2030×	`add-sqr-sqrt`
1608×	`times-frac`
1061×	`*-un-lft-identity`
765×	`sqrt-prod`
693×	`add-cube-cbrt`
463×	`associate-l`
460×	`difference-of-squares`
415×	`unswap-sqr`
279×	`associate-r`
185×	`*-commutative`
184×	`distribute-lft-out--`
180×	`prod-diff`
131×	`swap-sqr`
70×	`associate-/r*`
52×	`associate-/l*`
28×	`associate-/r/`
18×	`add-exp-log` `add-cbrt-cube`
15×	`fma-neg` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`sqrt-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1245

Calls

4 calls:

23.0ms	(/ (sqrt (- (* z z) (* t a))) z)
20.0ms	(- (* z z) (* t a))
49.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.0ms	(sqrt (- (* z z) (* t a)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sqrt (- (* z z) (* t a))) z)
40.0ms	(- (* z z) (* t a))
88.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify294.0ms

Algorithm

egg-herbie

Counts

1257 → 1257

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	3350	18401
1	5001	17037

prune1.4s

Filtered

1257 candidates to 478 candidates (62.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1253	4	1257
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	1258	7	1265

Merged error: 3.5b

Counts

1265 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* x 1) (/ (/ (sqrt (- (* z z) (* t a))) z) y))
1.4b	(- (* z z) (* t a))
1.5b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
23.7b	(sqrt (- (* z z) (* t a)))

rewrite645.0ms

Algorithm

rewrite-expression-head

Rules

8248×	`times-frac`
7230×	`add-sqr-sqrt`
4314×	`*-un-lft-identity`
2957×	`add-cube-cbrt`
2448×	`sqrt-prod`
1450×	`difference-of-squares`
1437×	`unswap-sqr`
1255×	`associate-l`
675×	`associate-r`
580×	`distribute-lft-out--`
515×	`*-commutative`
329×	`swap-sqr`
208×	`associate-/r*`
181×	`associate-/l*`
180×	`prod-diff`
98×	`associate-/r/`
63×	`div-inv`
60×	`associate-/l/`
39×	`add-exp-log`
30×	`add-cbrt-cube`
21×	`div-exp`
15×	`cbrt-undiv` `fma-neg`
6×	`sqrt-div` `prod-exp` `add-log-exp`
5×	`pow1` `frac-2neg` `clear-num`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`1-exp` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 3439

Calls

4 calls:

122.0ms	(/ (* x 1) (/ (/ (sqrt (- (* z z) (* t a))) z) y))
21.0ms	(- (* z z) (* t a))
38.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
26.0ms	(sqrt (- (* z z) (* t a)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* x 1) (/ (/ (sqrt (- (* z z) (* t a))) z) y))
39.0ms	(- (* z z) (* t a))
74.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
70.0ms	(sqrt (- (* z z) (* t a)))

simplify933.0ms

Algorithm

egg-herbie

Counts

3451 → 3451

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5001	63606

prune4.0s

Filtered

3451 candidates to 1126 candidates (67.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	3450	1	3451
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	3451	7	3458

Merged error: 3.5b

Counts

3458 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* x 1) (/ (/ (sqrt 1) 1) (/ y (/ (sqrt (- (* z z) (* t a))) z))))
1.4b	(- (* z z) (* t a))
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite17.5s

Algorithm

rewrite-expression-head

Rules

306704×	`times-frac`
196272×	`add-sqr-sqrt`
132710×	`*-un-lft-identity`
102531×	`add-cube-cbrt`
81718×	`sqrt-prod`
32063×	`unswap-sqr`
31470×	`difference-of-squares`
27681×	`associate-l`
15093×	`associate-r`
12588×	`distribute-lft-out--`
11325×	`*-commutative`
9921×	`associate-/r/`
7119×	`associate-/r*`
6333×	`swap-sqr`
6286×	`associate-/l*`
4407×	`div-inv`
632×	`associate-/l/`
622×	`sqrt-div`
328×	`frac-2neg` `clear-num`
312×	`flip3--` `flip--`
180×	`prod-diff`
142×	`add-exp-log`
105×	`div-exp`
74×	`add-cbrt-cube`
47×	`cbrt-undiv`
20×	`prod-exp`
19×	`1-exp`
15×	`fma-neg`
7×	`cbrt-unprod`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 70915

Calls

4 calls:

2.2s	(/ (* x 1) (/ (/ (sqrt 1) 1) (/ y (/ (sqrt (- (* z z) (* t a))) z))))
21.0ms	(- (* z z) (* t a))
37.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
27.0ms	(sqrt (- (* z z) (* t a)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* x 1) (/ (/ (sqrt 1) 1) (/ y (/ (sqrt (- (* z z) (* t a))) z))))
33.0ms	(- (* z z) (* t a))
58.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
71.0ms	(sqrt (- (* z z) (* t a)))

simplify22.6s

Algorithm

egg-herbie

Counts

70927 → 70927

Iterations

Useful iterations: 0 (1.2s)

Iter	Nodes	Cost
0	51323	2131447

prune3.2m

Filtered

70927 candidates to 34056 candidates (52.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	70926	1	70927
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	70926	8	70934

Merged error: 3.5b

Counts

70934 → 8

regimes341.0ms

Accuracy

85.8% (2.7b remaining)

Error of 6.1b against oracle of 3.4b and baseline of 22.4b

bsearch88.0ms

Steps

Iters	Range		Point
7	5.980436183971059e+94	9.936034952497785e+95	9.681419240575677e+95
9	-8.996402344186238e+125	-1.8490705375745513e+120	-8.62164551794021e+125

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	11
1	40	11
2	45	11
3	45	11

end0.0ms

sample788.0ms

Algorithm

intervals

Results

338.0ms	8818×	body	80	valid
103.0ms	2894×	body	80	nan