Details

sample317.0ms

Algorithm

intervals

Results

11.0ms	39×	body	2560	valid
8.0ms	180×	body	80	valid
4.0ms	27×	body	640	valid
4.0ms	20×	body	1280	valid
4.0ms	91×	body	80	nan
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	5×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

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: 35.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

14.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune320.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	9	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Merged error: 3.3b

Counts

184 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	770	4550
1	3215	3424
2	5002	3236

prune306.0ms

Filtered

269 candidates to 110 candidates (40.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	266	3	269
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	270	8	278

Merged error: 3.2b

Counts

278 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

14.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	609	2986
1	2322	1993
2	5001	1940

prune260.0ms

Filtered

181 candidates to 96 candidates (53.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	181	8	189

Merged error: 3.2b

Counts

189 → 8

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

6.0ms

(* -1/2 (/ c b_2))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(* -1/2 (/ c b_2))

simplify66.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	166	134
1	729	124
2	2966	124
3	5001	124

prune50.0ms

Filtered

37 candidates to 26 candidates (70.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	34	11	45

Merged error: 3.2b

Counts

45 → 11

regimes210.0ms

Accuracy

83.6% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.7b

bsearch209.0ms

Steps

Iters	Range		Point
10	1.5450168366677492e+128	2.0521185469434633e+142	3.9701546350182474e+129
11	-1.0303076794227059e-155	-1.0133968715090831e-176	-9.097853122909879e-156
5	-1.4643227903530048e-124	-6.030931541348017e-125	-6.313023766163172e-125
9	-2.2447030685571666e-91	-2.829998530983053e-96	-1.3786658632014202e-92

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	32
1	51	32
2	51	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1063×	body	2560	valid
252.0ms	5803×	body	80	valid
190.0ms	920×	body	1280	valid
122.0ms	2975×	body	80	nan
72.0ms	465×	body	640	valid
36.0ms	123×	body	5120	valid
28.0ms	236×	body	320	valid
10.0ms	124×	body	160	valid