Details

sample280.0ms

Algorithm

intervals

Results

8.0ms	202×	body	80	valid
5.0ms	35×	body	1280	valid
5.0ms	27×	body	2560	valid
3.0ms	86×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

43.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune252.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
27.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
153.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
187.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune495.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

3063×	`times-frac`
1689×	`add-sqr-sqrt`
1446×	`*-un-lft-identity`
1204×	`add-cube-cbrt`
242×	`difference-of-squares`
237×	`associate-/l*`
124×	`sqrt-prod`
121×	`distribute-lft-out--`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1025

Calls

4 calls:

40.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
66.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify244.0ms

Algorithm

egg-herbie

Counts

1037 → 1037

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	4265	21068
1	5002	20476

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
10.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
52×	`times-frac`
51×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 141

Calls

4 calls:

19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
24.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
152.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
187.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	700	1780
1	3210	1574
2	5002	1559

prune346.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes153.0ms

Accuracy

88.6% (3.0b remaining)

Error of 8.7b against oracle of 5.7b and baseline of 31.8b

bsearch121.0ms

Steps

Iters	Range	Point
8	2.1878188410446244e+107	3.8616146939177386e+111	2.0393047436202585e+111
10	-1.748936198008001e-296	1.7693602656524167e-306	-3.825646522708247e-308
6	-2.1205983461440786e-16	-4.95051961110899e-17	-1.954602026155351e-16

Iters

Range

Point

2.1878188410446244e+107

3.8616146939177386e+111

2.0393047436202585e+111

-1.748936198008001e-296

1.7693602656524167e-306

-3.825646522708247e-308

-2.1205983461440786e-16

-4.95051961110899e-17

-1.954602026155351e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample982.0ms

Algorithm

intervals

Results

206.0ms	1110×	body	2560	valid
185.0ms	5789×	body	80	valid
142.0ms	885×	body	1280	valid
86.0ms	2997×	body	80	nan
52.0ms	449×	body	640	valid
23.0ms	102×	body	5120	valid
22.0ms	256×	body	320	valid
7.0ms	124×	body	160	valid