Details

sample49.0ms

Algorithm

intervals

Results

10.0ms	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	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
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)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

17.0ms	(* (* 4.0 a) c)
11.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* 4.0 a) c)
41.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune182.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize18.0ms

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)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

24.0ms	(- (- 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))
60.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
130.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
162.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
61.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2427

prune445.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize17.0ms

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)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* 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)))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune224.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) 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)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
108×	`div-exp`
56×	`prod-exp`
49×	`add-cbrt-cube`
37×	`1-exp`
31×	`times-frac`
24×	`add-sqr-sqrt`
23×	`cbrt-undiv` `*-un-lft-identity`
19×	`add-cube-cbrt`
13×	`associate-/l*`
12×	`rec-exp` `cbrt-unprod`
10×	`add-log-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod`
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` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

58.0ms	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
41.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify97.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	907	1941
1	4224	1560
2	5001	1525

prune253.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

regimes168.0ms

Accuracy

94.1% (1.3b remaining)

Error of 8.6b against oracle of 7.3b and baseline of 29.3b

bsearch225.0ms

Steps

Iters	Range	Point
9	2.5943009456277367e+151	2.863179527023367e+158	1.3257937988037266e+154
11	-1.5799869936663156e-158	-6.164197719833672e-182	-6.278504568756145e-182
9	-2.3517657564579724e+121	-1.0016636615098116e+114	-1.78846664658268e+121

Iters

Range

Point

2.5943009456277367e+151

2.863179527023367e+158

1.3257937988037266e+154

-1.5799869936663156e-158

-6.164197719833672e-182

-6.278504568756145e-182

-2.3517657564579724e+121

-1.0016636615098116e+114

-1.78846664658268e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	49
1	67	49
2	69	49
3	69	49

end0.0ms

sample1.2s

Algorithm

intervals

Results

234.0ms	1059×	body	2560	valid
225.0ms	5787×	body	80	valid
163.0ms	896×	body	1280	valid
107.0ms	2934×	body	80	nan
74.0ms	490×	body	640	valid
33.0ms	114×	body	5120	valid
25.0ms	228×	body	320	valid
9.0ms	120×	body	160	valid