Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	186×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	82×	body	80	nan
2.0ms	8×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	6×	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	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune288.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 232

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
26.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
146.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
173.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	825	5119
1	3738	3863
2	5001	3860

prune699.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

8.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
21×	`times-frac`
19×	`add-cube-cbrt`
13×	`sqrt-prod`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `distribute-rgt-neg-in` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 100

Calls

4 calls:

26.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	363	1311
1	1840	1237
2	5001	1228

prune454.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize30.0ms

Local error

Found 4 expressions with local error:

16.2b	(- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

90×	`prod-diff`
76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
67×	`add-cube-cbrt`
62×	`log-prod` `exp-sum`
40×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
10×	`neg-mul-1` `fma-neg`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
2×	`diff-log` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 172

Calls

4 calls:

21.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	493	5009
1	1440	2563
2	5001	2438

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

regimes353.0ms

Accuracy

82.5% (4.9b remaining)

Error of 10.4b against oracle of 5.4b and baseline of 33.7b

bsearch133.0ms

Steps

Iters	Range		Point
10	4.734590495924167e-35	7.237368999400794e-22	8.870690604736125e-35
11	-1.1860998636736231e+119	-1.6133553378404837e+99	-3.7171108546007633e+118

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	23
1	35	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

246.0ms	1074×	body	2560	valid
230.0ms	5830×	body	80	valid
162.0ms	901×	body	1280	valid
104.0ms	2961×	body	80	nan
64.0ms	453×	body	640	valid
27.0ms	256×	body	320	valid
25.0ms	91×	body	5120	valid
11.0ms	121×	body	160	valid