Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	280×	body	80	valid
4.0ms	102×	body	80	nan

simplify11.0ms

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

prune3.0ms

Filtered

1 candidates to 0 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: 24.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
9.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
10.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
78.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	368	630
1	1941	560
2	5001	551

prune239.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	87	11	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	12	99

Merged error: 4.7b

Counts

99 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
2.3b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 142

Calls

4 calls:

6.0ms	(/ (sqrt (- (* z z) (* t a))) z)
4.0ms	(- (* z z) (* t a))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (sqrt (- (* z z) (* t a))) z)
39.0ms	(- (* z z) (* t a))
86.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
55.0ms	(sqrt (- (* z z) (* t a)))

simplify100.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	543	1379
1	2448	1281
2	5001	1260

prune328.0ms

Filtered

154 candidates to 109 candidates (70.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	155	11	166

Merged error: 4.5b

Counts

166 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
0.6b	(- (* z z) (* t a))
2.3b	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
30×	`add-cbrt-cube`
29×	`add-sqr-sqrt`
17×	`prod-exp`
16×	`*-un-lft-identity` `div-exp`
14×	`add-cube-cbrt` `times-frac`
13×	`associate-r`
10×	`sqrt-div`
9×	`cbrt-undiv` `sqrt-prod` `cbrt-unprod`
7×	`pow1`
6×	`flip3--` `associate-l` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 118

Calls

4 calls:

11.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
4.0ms	(- (* z z) (* t a))
13.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
33.0ms	(- (* z z) (* t a))
76.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify78.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	570	1066
1	2775	940
2	5001	915

prune260.0ms

Filtered

130 candidates to 88 candidates (67.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	130	11	141

Merged error: 4.5b

Counts

141 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.0b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
3.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 237

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
10.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
23.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
7.0ms	(sqrt (- (* z z) (* t a)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
52.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
84.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify107.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	839	2556
1	4071	2400
2	5002	2396

prune529.0ms

Filtered

249 candidates to 171 candidates (68.7%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	249	11	260

Merged error: 4.5b

Counts

260 → 11

regimes368.0ms

Accuracy

85.3% (3.0b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 23.5b

bsearch141.0ms

Steps

Iters	Range	Point
7	4.904842434366931e+136	2.583983515518581e+138	1.998388355114222e+137
8	-5.198330287526027e-251	-6.309453960374173e-254	-8.504918652399411e-253
9	-3.291745184388977e+160	-2.9340887831229106e+153	-6.761458302909995e+153

Iters

Range

Point

4.904842434366931e+136

2.583983515518581e+138

1.998388355114222e+137

-5.198330287526027e-251

-6.309453960374173e-254

-8.504918652399411e-253

-3.291745184388977e+160

-2.9340887831229106e+153

-6.761458302909995e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	36	17
2	36	17

end0.0ms

sample792.0ms

Algorithm

intervals

Results

340.0ms	8850×	body	80	valid
107.0ms	2933×	body	80	nan