Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
6.0ms	34×	body	1280	valid
5.0ms	25×	body	2560	valid
4.0ms	115×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	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: 35.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite109.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune299.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite184.0ms

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:

29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms	(/ (/ (+ 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))))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
170.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (92.0ms)

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

prune510.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.7b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

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)))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify84.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (63.0ms)

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

prune303.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
64×	`add-exp-log` `*-un-lft-identity`
61×	`prod-diff`
60×	`add-cube-cbrt`
40×	`div-exp`
34×	`sqrt-prod`
31×	`times-frac`
25×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv` `fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `cbrt-unprod` `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 → 195

Calls

4 calls:

36.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
40.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	846	3812
1	3886	2561
2	5002	2521

prune350.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.7b

regimes133.0ms

Accuracy

94% (1.4b remaining)

Error of 6.8b against oracle of 5.4b and baseline of 29.4b

bsearch159.0ms

Steps

Iters	Range	Point
9	1.7695728335377845e+74	3.738006738925262e+80	2.0572050780400815e+80
6	-3.405927582379186e-150	-4.860750269204613e-151	-4.9276367402926466e-151
7	-3.260864156300871e+111	-2.161458270686658e+109	-2.3929031452945402e+111

Iters

Range

Point

1.7695728335377845e+74

3.738006738925262e+80

2.0572050780400815e+80

-3.405927582379186e-150

-4.860750269204613e-151

-4.9276367402926466e-151

-3.260864156300871e+111

-2.161458270686658e+109

-2.3929031452945402e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	40
1	51	40

end0.0ms

sample1.2s

Algorithm

intervals

Results

235.0ms	1059×	body	2560	valid
217.0ms	5787×	body	80	valid
167.0ms	896×	body	1280	valid
106.0ms	2934×	body	80	nan
68.0ms	490×	body	640	valid
30.0ms	114×	body	5120	valid
28.0ms	228×	body	320	valid
8.0ms	120×	body	160	valid