Details

sample49.0ms

Algorithm

intervals

Results

10.0ms	199×	body	80	valid
7.0ms	24×	body	2560	valid
6.0ms	25×	body	1280	valid
6.0ms	15×	body	640	valid
4.0ms	79×	body	80	nan
2.0ms	6×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

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

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: 31.9b

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)))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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:

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))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune218.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Merged error: 4.5b

Counts

90 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
46.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune201.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 4.5b

Counts

103 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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:

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

series312.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	533	1804
1	2544	1605
2	5002	1531

prune230.0ms

Filtered

137 candidates to 73 candidates (53.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Merged error: 4.4b

Counts

144 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
13.2b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`times-frac` `distribute-lft-out` `associate-/l*`
3×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`flip3--` `sqrt-div` `associate-*l/` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 71

Calls

4 calls:

8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
167.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify106.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	502	969
1	3079	812
2	5002	794

prune404.0ms

Filtered

83 candidates to 62 candidates (74.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	82	8	90

Merged error: 4.4b

Counts

90 → 8

regimes185.0ms

Accuracy

86.6% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 34.4b

bsearch197.0ms

Steps

Iters	Range	Point
7	3.0106008231332273e+28	3.853441604264477e+30	1.1044936555910329e+30
9	-2.429997164111867e-152	-2.524662530443369e-160	-3.5042457694696975e-155
8	-3.6008568149396615e+78	-3.5390459793015956e+75	-8.575966285465455e+75

Iters

Range

Point

3.0106008231332273e+28

3.853441604264477e+30

1.1044936555910329e+30

-2.429997164111867e-152

-2.524662530443369e-160

-3.5042457694696975e-155

-3.6008568149396615e+78

-3.5390459793015956e+75

-8.575966285465455e+75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	48	31

end0.0ms

sample1.5s

Algorithm

intervals

Results

317.0ms	1067×	body	2560	valid
316.0ms	5859×	body	80	valid
228.0ms	893×	body	1280	valid
149.0ms	2863×	body	80	nan
94.0ms	457×	body	640	valid
39.0ms	106×	body	5120	valid
38.0ms	240×	body	320	valid
11.0ms	108×	body	160	valid