Details

sample51.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
9.0ms	181×	body	80	valid
6.0ms	27×	body	1280	valid
5.0ms	101×	body	80	nan
4.0ms	21×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 35.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

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:

11.0ms	(/ (+ (- 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))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (43.0ms)

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

prune266.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 6.3b

Counts

103 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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)))))
21.0ms	(/ (/ (+ 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))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify144.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (99.0ms)

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

prune478.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	242	10	252

Merged error: 6.2b

Counts

252 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.5b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

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` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `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 → 152

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
146.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify104.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	655	3361
1	3267	2163
2	5002	2073

prune271.0ms

Filtered

164 candidates to 82 candidates (50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	4	4	8
Picked	0	1	1
Done	1	0	1
Total	167	7	174

Merged error: 6.2b

Counts

174 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
0.6b	(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
14.0ms	(- (- 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:

49.0ms	(- (* b b) (* 4.0 (* a c)))
120.0ms	(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	725	3603
1	2796	2445
2	5001	2404

prune343.0ms

Filtered

186 candidates to 105 candidates (56.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	184	9	193

Merged error: 6.2b

Counts

193 → 9

regimes194.0ms

Accuracy

94.8% (1.3b remaining)

Error of 7.2b against oracle of 5.9b and baseline of 30.4b

bsearch181.0ms

Steps

Iters	Range	Point
6	6.333441064762502e+69	2.6854631551896503e+70	2.6627070202833933e+70
8	-1.820258497722058e-231	-5.550307098040058e-234	-5.631981429033553e-234
8	-1.666412824726956e+124	-3.415589734864014e+119	-5.377788818048344e+121

Iters

Range

Point

6.333441064762502e+69

2.6854631551896503e+70

2.6627070202833933e+70

-1.820258497722058e-231

-5.550307098040058e-234

-5.631981429033553e-234

-1.666412824726956e+124

-3.415589734864014e+119

-5.377788818048344e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	28
1	51	28
2	51	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

308.0ms	5875×	body	80	valid
308.0ms	1055×	body	2560	valid
216.0ms	902×	body	1280	valid
140.0ms	2921×	body	80	nan
86.0ms	426×	body	640	valid
35.0ms	100×	body	5120	valid
34.0ms	242×	body	320	valid
10.0ms	106×	body	160	valid