Details

sample55.0ms

Algorithm

intervals

Results

10.0ms	196×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	24×	body	1280	valid
4.0ms	87×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	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: 33.2b

Counts

2 → 1

localize16.0ms

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))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
58.0ms	(- (* b b) (* (* 4.0 a) c))
99.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune368.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	6	83

Merged error: 6.4b

Counts

83 → 6

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))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
59.0ms	(- (* b b) (* (* 4.0 a) c))
99.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	528	1585
1	2596	1372
2	5001	1305

prune481.0ms

Filtered

126 candidates to 72 candidates (42.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	124	8	132

Merged error: 6.3b

Counts

132 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
279.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
350.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	646	2693
1	3163	2447
2	5003	2434

prune1.2s

Filtered

166 candidates to 110 candidates (33.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	167	7	174

Merged error: 6.3b

Counts

174 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`flip3--` `sqrt-prod` `flip--`
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` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

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

series524.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b b) (* (* 4.0 a) c))
93.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
281.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	486	953
1	2888	749
2	5001	741

prune478.0ms

Filtered

84 candidates to 58 candidates (31.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	85	6	91

Merged error: 6.3b

Counts

91 → 6

regimes371.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.7b

bsearch276.0ms

Steps

Iters	Range	Point
9	5.514542683406611e+77	2.3545344307669661e+86	5.916921414433248e+85
9	-1.015236884690783e-269	-1.3837509176949247e-276	-2.1500220158495505e-274
10	-1.5262535002821125e+142	-1.5364234610613206e+132	-1.4307617421379746e+138

Iters

Range

Point

5.514542683406611e+77

2.3545344307669661e+86

5.916921414433248e+85

-1.015236884690783e-269

-1.3837509176949247e-276

-2.1500220158495505e-274

-1.5262535002821125e+142

-1.5364234610613206e+132

-1.4307617421379746e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	49	27
2	49	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

310.0ms	1056×	body	2560	valid
298.0ms	5861×	body	80	valid
215.0ms	909×	body	1280	valid
145.0ms	2908×	body	80	nan
87.0ms	467×	body	640	valid
40.0ms	112×	body	5120	valid
32.0ms	229×	body	320	valid
10.0ms	105×	body	160	valid

Details

sample55.0ms

simplify10.0ms

prune5.0ms

localize16.0ms

rewrite27.0ms

series421.0ms

simplify46.0ms

prune368.0ms

localize13.0ms

rewrite34.0ms

series483.0ms

simplify71.0ms

prune481.0ms

localize16.0ms

rewrite48.0ms

series817.0ms

simplify117.0ms

prune1.2s

localize17.0ms

rewrite31.0ms

series524.0ms

simplify72.0ms

prune478.0ms

regimes371.0ms

bsearch276.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling