Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	209×	body	80	valid
8.0ms	34×	body	2560	valid
4.0ms	22×	body	1280	valid
3.0ms	79×	body	80	nan
3.0ms	18×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

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:

32.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune229.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
40.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
28.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
192.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320

prune418.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
14.1b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `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 → 70

Calls

4 calls:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune221.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
108×	`div-exp`
56×	`prod-exp`
49×	`add-cbrt-cube`
37×	`1-exp`
31×	`times-frac`
24×	`add-sqr-sqrt`
23×	`cbrt-undiv` `*-un-lft-identity`
19×	`add-cube-cbrt`
13×	`associate-/l*`
12×	`rec-exp` `cbrt-unprod`
10×	`add-log-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

29.0ms	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	907	1941
1	4224	1560
2	5001	1525

prune240.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes246.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.3b

bsearch185.0ms

Steps

Iters	Range	Point
8	1.9559514031553493e+101	2.0413668072230428e+104	9.373511171447418e+103
9	1.0311906074547519e-259	1.091011630730822e-254	1.0417939395900796e-259
9	-2.3467190644739184e+107	-3.2019781887028674e+101	-1.7431685240570133e+102

Iters

Range

Point

1.9559514031553493e+101

2.0413668072230428e+104

9.373511171447418e+103

1.0311906074547519e-259

1.091011630730822e-254

1.0417939395900796e-259

-2.3467190644739184e+107

-3.2019781887028674e+101

-1.7431685240570133e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	50	27
2	50	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

279.0ms	1070×	body	2560	valid
248.0ms	5839×	body	80	valid
187.0ms	884×	body	1280	valid
116.0ms	2849×	body	80	nan
79.0ms	496×	body	640	valid
32.0ms	102×	body	5120	valid
26.0ms	220×	body	320	valid
8.0ms	103×	body	160	valid