Details

sample74.0ms

Algorithm

intervals

Results

17.0ms	35×	body	2560	valid
15.0ms	189×	body	80	valid
11.0ms	27×	body	1280	valid
8.0ms	101×	body	80	nan
5.0ms	17×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	5120	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize15.0ms

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)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

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:

32.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune794.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite98.0ms

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:

17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
40.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
39.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify131.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (93.0ms)

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

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt`
10×	`fma-def` `prod-exp` `add-log-exp`
7×	`pow1` `associate-r`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

51.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	515	1011
1	2277	856
2	5001	843

prune831.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
48×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
8×	`distribute-rgt-neg-in`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 134

Calls

4 calls:

24.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	556	1665
1	2664	1442
2	5002	1371

prune917.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes331.0ms

Accuracy

81.7% (4.9b remaining)

Error of 10.7b against oracle of 5.8b and baseline of 32.4b

bsearch87.0ms

Steps

Iters	Range		Point
10	2.922623675251237e-45	3.998186072825638e-35	8.679707852111266e-40
8	-6.30521239297407e+53	-2.0681333037085905e+50	-4.837192574744688e+53

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

505.0ms	1039×	body	2560	valid
478.0ms	5877×	body	80	valid
362.0ms	910×	body	1280	valid
225.0ms	2874×	body	80	nan
147.0ms	463×	body	640	valid
64.0ms	112×	body	5120	valid
54.0ms	230×	body	320	valid
16.0ms	103×	body	160	valid