Details

sample50.0ms

Algorithm

intervals

Results

10.0ms	139×	body	160	valid
10.0ms	529×	pre	80	true
9.0ms	273×	body	80	nan
4.0ms	117×	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: 27.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
27.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite35.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

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

prune269.0ms

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: 0.3b

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

rewrite58.0ms

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:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify159.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (120.0ms)

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

prune582.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	231	12	243
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	236	12	248

Merged error: 0.0b

Counts

248 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

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)))))
15.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
9.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
11.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
155.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
89.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify134.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (88.0ms)

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

prune545.0ms

Filtered

242 candidates to 132 candidates (54.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	234	8	242
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	244	10	254

Merged error: 0.0b

Counts

254 → 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))))))
0.2b	(* a (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
0.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

180×	`prod-diff`
135×	`add-sqr-sqrt`
132×	`*-un-lft-identity`
124×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
19×	`neg-mul-1`
10×	`fma-neg` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `associate-l` `flip--`
2×	`diff-log` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 284

Calls

4 calls:

2.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
14.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
14.0ms	(* a (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
13.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
89.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
111.0ms	(* a (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
160.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

simplify146.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	734	8321
1	3687	5180
2	5002	4912

prune373.0ms

Filtered

296 candidates to 94 candidates (31.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	290	6	296
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	298	8	306

Merged error: 0b

Counts

306 → 8

regimes123.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	13
1	29	13
2	35	13
3	35	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

311.0ms	4450×	body	160	valid
311.0ms	16870×	pre	80	true
306.0ms	8870×	body	80	nan
130.0ms	3550×	body	80	valid