Details

sample72.0ms

Algorithm

intervals

Results

17.0ms	147×	body	160	valid
15.0ms	553×	pre	80	true
14.0ms	297×	body	80	nan
5.0ms	109×	body	80	valid

simplify12.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite33.0ms

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:

7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	855
1	1702	750
2	5002	735

prune237.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	5	103

Merged error: 0.4b

Counts

103 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`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`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
149.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828

prune539.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	233	10	243
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	238	10	248

Merged error: 0b

Counts

248 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.2b	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

rewrite51.0ms

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`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `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 → 230

Calls

4 calls:

2.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
9.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
19.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
11.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
86.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
187.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify125.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	767	5082
1	3166	3826
2	5001	3733

prune460.0ms

Filtered

242 candidates to 132 candidates (54.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	242	10	252

Merged error: 0b

Counts

252 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
121×	`prod-diff`
92×	`add-cbrt-cube`
90×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
73×	`prod-exp`
62×	`distribute-rgt-in` `distribute-lft-in`
61×	`sqrt-prod`
46×	`div-exp`
41×	`cbrt-unprod`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
26×	`cbrt-undiv`
12×	`neg-mul-1`
9×	`pow1`
8×	`rec-exp` `1-exp`
7×	`associate-r`
6×	`add-log-exp`
5×	`flip3--` `times-frac` `associate-l` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `div-inv`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`fma-neg` `diff-log` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 269

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
23.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
142.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
79.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1280	7983
1	5001	5713

prune332.0ms

Filtered

281 candidates to 93 candidates (33.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	281	10	291

Merged error: 0b

Counts

291 → 10

regimes149.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	34	13
2	40	13
3	40	13

end0.0ms

sample1.9s

Algorithm

intervals

Results

456.0ms	16723×	pre	80	true
436.0ms	4428×	body	160	valid
425.0ms	8723×	body	80	nan
179.0ms	3572×	body	80	valid