Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	36×	body	2560	valid
7.0ms	180×	body	80	valid
6.0ms	75×	body	80	nan
4.0ms	24×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

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: 35.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
50.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune268.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 5.9b

Counts

103 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
159.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify138.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	818	5119
1	3560	3863
2	5001	3860

prune498.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	238	6	244
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	240	11	251

Merged error: 5.8b

Counts

251 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.5b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
8.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
71×	`add-cube-cbrt`
60×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg`
8×	`cbrt-undiv` `cbrt-unprod` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 227

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
153.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
198.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify156.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	910	4844
1	4351	3468
2	5001	3468

prune439.0ms

Filtered

239 candidates to 128 candidates (53.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	4	4	8
Picked	0	1	1
Done	1	1	2
Total	242	8	250

Merged error: 5.8b

Counts

250 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.9b	(/ (* 4.0 (* a c)) (* 2.0 a))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	604	3032
1	2957	1948
2	5001	1867

prune242.0ms

Filtered

162 candidates to 79 candidates (48.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	164	6	170

Merged error: 5.8b

Counts

170 → 6

regimes435.0ms

Accuracy

93.2% (1.6b remaining)

Error of 7.0b against oracle of 5.4b and baseline of 29.4b

bsearch193.0ms

Steps

Iters	Range	Point
9	1.314833454423355e+61	1.6016599845544569e+66	7.7076257484328935e+65
10	-4.4782599006234366e-147	-2.1964053429920463e-160	-2.2271387790640654e-160
10	-1.5021501144069279e+69	-2.501148282372368e+59	-1.2963688795759268e+64

Iters

Range

Point

1.314833454423355e+61

1.6016599845544569e+66

7.7076257484328935e+65

-4.4782599006234366e-147

-2.1964053429920463e-160

-2.2271387790640654e-160

-1.5021501144069279e+69

-2.501148282372368e+59

-1.2963688795759268e+64

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

239.0ms	5827×	body	80	valid
237.0ms	1049×	body	2560	valid
166.0ms	883×	body	1280	valid
108.0ms	2908×	body	80	nan
73.0ms	486×	body	640	valid
28.0ms	92×	body	5120	valid
27.0ms	244×	body	320	valid
10.0ms	129×	body	160	valid