Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	192×	body	80	valid
7.0ms	32×	body	2560	valid
5.0ms	26×	body	1280	valid
3.0ms	71×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize14.0ms

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)))
2.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

32.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune245.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.5b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.1b	(- (pow b 2) (pow b 2))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
78×	`times-frac`
68×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`difference-of-squares`
27×	`associate-/l*`
22×	`unpow-prod-down`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`sqrt-prod`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`div-sub` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

176.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
163.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
11.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
149.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify175.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (151.0ms)

Iter	Nodes	Cost
0	761	2839
1	3905	2393
2	5002	2366

prune482.0ms

Filtered

187 candidates to 123 candidates (65.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.7b	(/ (* 4.0 (* a c)) a)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(/ (* 4.0 (* a c)) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(/ (* 4.0 (* a c)) a)
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	344	518
1	1520	468
2	5001	450

prune202.0ms

Filtered

77 candidates to 54 candidates (70.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

20.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
3.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
43.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	346	764
1	1376	681
2	5001	678

prune216.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.7b

regimes165.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.8b

bsearch152.0ms

Steps

Iters	Range		Point
6	4.659640959833754e+64	2.871891476161473e+65	2.829212443283286e+65
8	1.9821308391676102e-213	4.8066894378040416e-210	2.5367024198462834e-213
7	-8.31287647374507e+123	-3.383610052221448e+122	-6.616177147650416e+122

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	25
1	46	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

256.0ms	1072×	body	2560	valid
244.0ms	5884×	body	80	valid
167.0ms	874×	body	1280	valid
111.0ms	2965×	body	80	nan
75.0ms	482×	body	640	valid
32.0ms	100×	body	5120	valid
28.0ms	221×	body	320	valid
9.0ms	116×	body	160	valid