Details

sample72.0ms

Algorithm

intervals

Results

19.0ms	160×	body	160	valid
14.0ms	502×	pre	80	true
12.0ms	246×	body	80	nan
6.0ms	40×	body	320	valid
3.0ms	56×	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: 44.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite31.0ms

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

series319.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms	(- (* b b) (* (* 4.0 a) c))
117.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5002	735

prune251.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	4	103

Merged error: 0.2b

Counts

103 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- 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))

series469.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify157.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (118.0ms)

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

prune541.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	236	7	243
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	238	9	247

Merged error: 0b

Counts

247 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

180×	`prod-diff`
152×	`add-exp-log`
135×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
92×	`sqrt-prod` `add-cbrt-cube`
73×	`prod-exp`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
46×	`div-exp`
41×	`cbrt-unprod`
26×	`cbrt-undiv`
19×	`neg-mul-1`
10×	`fma-neg`
9×	`pow1`
8×	`rec-exp` `1-exp` `add-log-exp`
7×	`associate-r`
5×	`flip3--` `times-frac` `associate-l` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `log1p-expm1-u` `associate-/l` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `div-inv`
2×	`pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `associate-/r`
1×	`associate--l-` `neg-sub0` `neg-log` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 343

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
18.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
151.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
91.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1248	10439
1	5002	7042

prune439.0ms

Filtered

355 candidates to 108 candidates (30.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	354	1	355
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	356	8	364

Merged error: 0b

Counts

364 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
77×	`add-cbrt-cube`
34×	`prod-exp` `cbrt-unprod`
21×	`add-sqr-sqrt`
20×	`div-exp`
19×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
15×	`times-frac`
8×	`sqrt-div` `distribute-neg-frac`
7×	`pow1` `associate-*l/` `associate-/r/`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r*` `sqrt-prod`
5×	`associate-l` `frac-add` `associate-/l*`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `div-inv` `distribute-lft-out` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`neg-mul-1` `rec-exp` `pow-flip` `flip3-+` `1-exp` `pow-prod-down` `*-commutative` `distribute-rgt-neg-out` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
12.0ms	(/ 1 (+ (* (/ (* 2.0 a) (* 4.0 (* a c))) (- b)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
16.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
184.0ms	(/ 1 (+ (* (/ (* 2.0 a) (* 4.0 (* a c))) (- b)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
132.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	813	2360
1	5002	1923

prune377.0ms

Filtered

163 candidates to 100 candidates (61.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	163	8	171

Merged error: 0b

Counts

171 → 8

regimes128.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	28	13
2	28	13

end0.0ms

sample2.0s

Algorithm

intervals

Results

465.0ms	16303×	pre	80	true
447.0ms	4767×	body	160	valid
387.0ms	8303×	body	80	nan
187.0ms	1360×	body	320	valid
91.0ms	1873×	body	80	valid