Details

sample43.0ms

Algorithm

intervals

Results

19.0ms	275×	body	80	valid
5.0ms	85×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	18

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: 20.7b

Counts

2 → 1

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
2.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	406	2988
1	1431	1956
2	5002	1869

prune383.0ms

Filtered

152 candidates to 80 candidates (52.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	142	10	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	10	153

Merged error: 7.0b

Counts

153 → 10

localize120.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.9b	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
6.1b	(/ (* a c) b)
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
60×	`prod-diff`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`times-frac` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u` `distribute-lft-out`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 161

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
19.0ms	(/ (* a c) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	650	3173
1	2665	2081
2	5002	2000

prune427.0ms

Filtered

173 candidates to 90 candidates (52.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	5	173
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	173	10	183

Merged error: 5.9b

Counts

183 → 10

localize113.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b	(- (* b b) (* (* 4.0 a) c))
2.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/r*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 156

Calls

4 calls:

11.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	545	3278
1	2114	2181
2	5002	2098

prune387.0ms

Filtered

168 candidates to 88 candidates (52.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	165	13	178

Merged error: 5.7b

Counts

178 → 13

localize119.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(- (* b b) (* (* 4.0 a) c))
2.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
61×	`prod-diff`
57×	`add-cube-cbrt`
37×	`sqrt-prod`
27×	`associate-r`
26×	`add-exp-log`
25×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
16×	`add-cbrt-cube`
12×	`prod-exp`
11×	`fma-neg`
10×	`pow1` `add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`neg-mul-1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
3×	`diff-log` `pow-prod-down`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 177

Calls

4 calls:

16.0ms	(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	690	3492
1	3003	2290
2	5001	2221

prune381.0ms

Filtered

189 candidates to 93 candidates (49.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	189	13	202

Merged error: 5.7b

Counts

202 → 13

regimes256.0ms

Accuracy

88.3% (1.8b remaining)

Error of 8.0b against oracle of 6.2b and baseline of 21.3b

bsearch163.0ms

Steps

Iters	Range		Point
7	4.4312058130773924e+95	1.951780157010812e+97	8.668740171701315e+95
9	-8.211399685419546e+34	-2.0557429965048975e+28	-8.122404781735759e+34

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	56
1	60	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

585.0ms	8699×	body	80	valid
197.0ms	2958×	body	80	nan