Details

sample55.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
9.0ms	183×	body	80	valid
6.0ms	28×	body	1280	valid
4.0ms	83×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune5.0ms

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: 34.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
57.0ms	(- (* b b) (* 4.0 (* a c)))
96.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune396.0ms

Filtered

89 candidates to 65 candidates (27.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 6.3b

Counts

90 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

14.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
57.0ms	(- (* b b) (* 4.0 (* a c)))
94.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
92.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune491.0ms

Filtered

137 candidates to 73 candidates (46.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	135	9	144

Merged error: 6.2b

Counts

144 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.1b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.3b	(- (pow b 2) (pow b 2))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
78×	`times-frac`
68×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`difference-of-squares`
27×	`associate-/l*`
22×	`unpow-prod-down`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`sqrt-prod`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`div-sub` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

27.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
25.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
206.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
92.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify193.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	760	2835
1	3914	2397
2	5002	2370

prune1.2s

Filtered

187 candidates to 124 candidates (33.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	188	8	196

Merged error: 6.2b

Counts

196 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.2b	(/ (* 4.0 (* a c)) a)
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod`
3×	`cbrt-undiv` `flip3--` `times-frac` `div-exp` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(/ (* 4.0 (* a c)) a)
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* 4.0 (* a c)))
99.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms	(/ (* 4.0 (* a c)) a)
91.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	340	517
1	1512	468
2	5002	450

prune352.0ms

Filtered

77 candidates to 54 candidates (29.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	77	8	85

Merged error: 6.2b

Counts

85 → 8

regimes349.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.8b

bsearch198.0ms

Steps

Iters	Range	Point
9	5.514542683406611e+77	2.3545344307669661e+86	1.5870501280763766e+84
2	3.778688962238916e-270	4.442120433279084e-270	3.855424616811019e-270
10	-1.5262535002821125e+142	-1.5364234610613206e+132	-6.152819208450137e+136

Iters

Range

Point

5.514542683406611e+77

2.3545344307669661e+86

1.5870501280763766e+84

3.778688962238916e-270

4.442120433279084e-270

3.855424616811019e-270

-1.5262535002821125e+142

-1.5364234610613206e+132

-6.152819208450137e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample1.5s

Algorithm

intervals

Results

315.0ms	1096×	body	2560	valid
285.0ms	5771×	body	80	valid
203.0ms	874×	body	1280	valid
133.0ms	2896×	body	80	nan
89.0ms	471×	body	640	valid
40.0ms	117×	body	5120	valid
33.0ms	243×	body	320	valid
10.0ms	109×	body	160	valid

Details

sample55.0ms

simplify12.0ms

prune5.0ms

localize11.0ms

rewrite32.0ms

series365.0ms

simplify47.0ms

prune396.0ms

localize13.0ms

rewrite36.0ms

series426.0ms

simplify67.0ms

prune491.0ms

localize19.0ms

rewrite74.0ms

series459.0ms

simplify193.0ms

prune1.2s

localize13.0ms

rewrite24.0ms

series259.0ms

simplify43.0ms

prune352.0ms

regimes349.0ms

bsearch198.0ms

simplify2.0ms

end0.0ms

sample1.5s

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