Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	189×	body	80	valid
7.0ms	28×	body	2560	valid
7.0ms	34×	body	1280	valid
4.0ms	92×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 35.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (43.0ms)

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

prune319.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
2.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* 4.0 (* a c)))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify117.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	665	2663
1	3259	2412
2	5001	2405

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
16.5b	(/ (* 2.0 a) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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:

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

series198.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (66.0ms)

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

prune298.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
108×	`div-exp`
65×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
61×	`prod-diff`
60×	`add-cube-cbrt`
56×	`prod-exp`
49×	`add-cbrt-cube`
37×	`1-exp`
34×	`sqrt-prod`
31×	`times-frac`
23×	`cbrt-undiv`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-/l*`
12×	`rec-exp` `cbrt-unprod`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 220

Calls

4 calls:

20.0ms	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(- (- 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))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (/ 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)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify129.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1089	4362
1	4800	2939
2	5001	2936

prune360.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

regimes145.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.8b against oracle of 5.8b and baseline of 29.8b

bsearch178.0ms

Steps

Iters	Range	Point
5	1.1874868645648804e+84	3.824179182553312e+84	3.347196852696382e+84
11	1.7635143872496245e-284	6.841012161467506e-264	1.7859783972070086e-284
8	-3.734333779790662e+128	-2.2987999557012895e+125	-5.238946631357967e+127

Iters

Range

Point

1.1874868645648804e+84

3.824179182553312e+84

3.347196852696382e+84

1.7635143872496245e-284

6.841012161467506e-264

1.7859783972070086e-284

-3.734333779790662e+128

-2.2987999557012895e+125

-5.238946631357967e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	34
1	52	34

end0.0ms

sample1.2s

Algorithm

intervals

Results

247.0ms	1050×	body	2560	valid
243.0ms	5875×	body	80	valid
178.0ms	905×	body	1280	valid
115.0ms	2863×	body	80	nan
70.0ms	457×	body	640	valid
28.0ms	99×	body	5120	valid
24.0ms	212×	body	320	valid
10.0ms	128×	body	160	valid