Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
7.0ms	186×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite114.0ms

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:

66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune293.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.1b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

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:

31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
86.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
155.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
191.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify129.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (92.0ms)

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

prune570.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

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:

9.0ms	(- (* b b) (* 4.0 (* a c)))
33.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify85.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (65.0ms)

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

prune310.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 173

Calls

4 calls:

98.0ms	(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	778	3604
1	3058	2345
2	5001	2298

prune335.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

regimes222.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.5b

bsearch163.0ms

Steps

Iters	Range	Point
7	1.2310742480127578e+144	1.3446930168628618e+146	1.458057835821772e+144
8	-4.3329860630795565e-185	-1.209307133318773e-187	-2.3517425397028646e-186
7	-2.3419197238566892e+109	-5.519096697972622e+107	-2.2237630570465103e+109

Iters

Range

Point

1.2310742480127578e+144

1.3446930168628618e+146

1.458057835821772e+144

-4.3329860630795565e-185

-1.209307133318773e-187

-2.3517425397028646e-186

-2.3419197238566892e+109

-5.519096697972622e+107

-2.2237630570465103e+109

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	36
1	48	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

230.0ms	5865×	body	80	valid
229.0ms	1052×	body	2560	valid
165.0ms	932×	body	1280	valid
105.0ms	2817×	body	80	nan
65.0ms	453×	body	640	valid
30.0ms	113×	body	5120	valid
24.0ms	235×	body	320	valid
8.0ms	120×	body	160	valid