Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	189×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	87×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune292.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

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:

19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
178.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify142.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	829	5119
1	3763	3863
2	5001	3860

prune553.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* 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)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify97.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	610	3042
1	3078	1945
2	5002	1857

prune320.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
41×	`div-exp`
34×	`sqrt-prod`
24×	`prod-exp` `add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`1-exp`
11×	`fma-neg`
10×	`cbrt-undiv` `add-log-exp`
8×	`pow1`
7×	`neg-mul-1` `rec-exp`
5×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
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 → 176

Calls

4 calls:

42.0ms	(/ 1 (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	792	3640
1	3189	2381
2	5002	2334

prune330.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

regimes226.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.2b against oracle of 5.3b and baseline of 29.8b

bsearch156.0ms

Steps

Iters	Range	Point
5	5.10808278574109e+145	1.867402505400959e+146	5.540445008636524e+145
8	-1.2523555155265933e-243	-3.6841099953537603e-246	-3.72191682831812e-246
7	-2.963931757502914e+119	-3.3757792073266624e+117	-8.003368877449752e+118

Iters

Range

Point

5.10808278574109e+145

1.867402505400959e+146

5.540445008636524e+145

-1.2523555155265933e-243

-3.6841099953537603e-246

-3.72191682831812e-246

-2.963931757502914e+119

-3.3757792073266624e+117

-8.003368877449752e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

242.0ms	1073×	body	2560	valid
225.0ms	5759×	body	80	valid
180.0ms	914×	body	1280	valid
114.0ms	2900×	body	80	nan
68.0ms	451×	body	640	valid
28.0ms	100×	body	5120	valid
25.0ms	229×	body	320	valid
10.0ms	132×	body	160	valid