Details

sample42.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
7.0ms	189×	body	80	valid
6.0ms	31×	body	1280	valid
4.0ms	104×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune294.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

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:

10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify130.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	818	5119
1	3560	3863
2	5001	3860

prune527.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.6b	(/ (* 2.0 a) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 150

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify93.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	597	3032
1	2832	1946
2	5002	1857

prune307.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
144×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`associate-l`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sqrt-div` `associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 289

Calls

4 calls:

19.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify128.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	928	8466
1	3529	5475
2	5002	5159

prune390.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes175.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.8b

bsearch198.0ms

Steps

Iters	Range	Point
9	1.846147638884188e+104	1.7844061428947563e+109	1.55563303224959e+106
9	-2.9188174999700146e-273	-1.0308405028667604e-278	-2.3730540219645598e-278
9	-3.3506371122085595e+158	-5.17073721832495e+150	-5.585435738628103e+150

Iters

Range

Point

1.846147638884188e+104

1.7844061428947563e+109

1.55563303224959e+106

-2.9188174999700146e-273

-1.0308405028667604e-278

-2.3730540219645598e-278

-3.3506371122085595e+158

-5.17073721832495e+150

-5.585435738628103e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

262.0ms	1102×	body	2560	valid
235.0ms	5879×	body	80	valid
173.0ms	882×	body	1280	valid
110.0ms	2998×	body	80	nan
64.0ms	418×	body	640	valid
34.0ms	118×	body	5120	valid
29.0ms	236×	body	320	valid
12.0ms	124×	body	160	valid