Details

sample58.0ms

Algorithm

intervals

Results

14.0ms	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

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

series435.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
56.0ms	(- (* b b) (* 4.0 (* a c)))
104.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune370.0ms

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

localize15.0ms

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))))

rewrite32.0ms

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)))))))
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))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
60.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
96.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	525	1585
1	2550	1372
2	5001	1305

prune471.0ms

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

localize14.0ms

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))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series849.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
292.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
364.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	635	2693
1	2974	2447
2	5001	2434

prune982.0ms

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

localize14.0ms

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))))

rewrite32.0ms

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:

4.0ms	(- (* 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))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b b) (* 4.0 (* a c)))
100.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
292.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	470	942
1	2684	750
2	5002	742

prune509.0ms

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

regimes368.0ms

Accuracy

95.3% (1.1b remaining)

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

bsearch271.0ms

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

314.0ms	1056×	body	2560	valid
305.0ms	5861×	body	80	valid
221.0ms	909×	body	1280	valid
143.0ms	2908×	body	80	nan
92.0ms	467×	body	640	valid
39.0ms	112×	body	5120	valid
32.0ms	229×	body	320	valid
13.0ms	105×	body	160	valid

Details

sample58.0ms

simplify10.0ms

prune5.0ms

localize11.0ms

rewrite27.0ms

series435.0ms

simplify46.0ms

prune370.0ms

localize15.0ms

rewrite32.0ms

series489.0ms

simplify68.0ms

prune471.0ms

localize14.0ms

rewrite48.0ms

series849.0ms

simplify105.0ms

prune982.0ms

localize14.0ms

rewrite32.0ms

series549.0ms

simplify67.0ms

prune509.0ms

regimes368.0ms

bsearch271.0ms

simplify2.0ms

end0.0ms

sample1.6s

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