Details

sample42.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
7.0ms	185×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	97×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	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: 34.8b

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))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(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))
3.0ms	(- (* 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))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

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

prune255.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 5.8b

Counts

90 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(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))
3.0ms	(- (* 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))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* 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))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune253.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 5.8b

Counts

98 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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:

16.0ms	(* (- (- 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)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

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

prune426.0ms

Filtered

97 candidates to 64 candidates (66.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	98	7	105

Merged error: 5.8b

Counts

105 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
15.4b	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
19.0b	(- (pow b 2) (pow b 2))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`add-exp-log`
22×	`unpow-prod-down`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt` `difference-of-squares`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `prod-exp`
8×	`distribute-lft-out--` `add-log-exp`
7×	`pow1` `associate-l`
4×	`div-exp` `cbrt-unprod`
3×	`flip3--` `times-frac` `associate-r` `sqrt-prod` `flip--`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `flip3-+` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `+-inverses` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

6.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
8.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
1.0ms	(- (pow b 2) (pow b 2))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify341.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (331.0ms)

Iter	Nodes	Cost
0	591	781
1	4612	569
2	5001	561

prune314.0ms

Filtered

123 candidates to 76 candidates (61.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	123	7	130

Merged error: 5.7b

Counts

130 → 7

regimes219.0ms

Accuracy

96% (1.0b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.4b

bsearch184.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.0673291895585486e+103
11	1.8145151230270015e-269	9.272403512084269e-250	1.6944972861664959e-264
6	-1.2994787762702041e+157	-3.0529494422842112e+156	-3.0812943354752785e+156

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.0673291895585486e+103

1.8145151230270015e-269

9.272403512084269e-250

1.6944972861664959e-264

-1.2994787762702041e+157

-3.0529494422842112e+156

-3.0812943354752785e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	28
1	59	28
2	59	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

262.0ms	1054×	body	2560	valid
245.0ms	5924×	body	80	valid
176.0ms	898×	body	1280	valid
110.0ms	2939×	body	80	nan
67.0ms	438×	body	640	valid
33.0ms	113×	body	5120	valid
23.0ms	199×	body	320	valid
10.0ms	131×	body	160	valid