Details

sample300.0ms

Algorithm

intervals

Results

11.0ms	209×	body	80	valid
6.0ms	32×	body	1280	valid
6.0ms	25×	body	2560	valid
4.0ms	103×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

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: 28.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune226.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 3.5b

Counts

93 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

17.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
33.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	569	2100
1	2561	1900
2	5002	1763

prune256.0ms

Filtered

174 candidates to 86 candidates (49.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	173	9	182

Merged error: 3.5b

Counts

182 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

21.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
33.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1686	7575
1	5001	6811

prune555.0ms

Filtered

435 candidates to 171 candidates (39.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	435	9	444

Merged error: 3.5b

Counts

444 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.4b	(sqrt (- (* b_2 b_2) (* a c)))
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	210	520
1	734	480
2	2511	458
3	5001	454

prune201.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 3.5b

Counts

81 → 9

regimes178.0ms

Accuracy

88.7% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 33.8b

bsearch149.0ms

Steps

Iters	Range	Point
9	1.7536266209730185e+54	9.156208036690931e+61	2.5096626454411205e+56
10	8.752895080382474e-191	7.198562597133285e-172	2.5184045435465955e-179
4	-2.2709498629311444e+153	-1.3123487377944479e+153	-1.5396067403637575e+153

Iters

Range

Point

1.7536266209730185e+54

9.156208036690931e+61

2.5096626454411205e+56

8.752895080382474e-191

7.198562597133285e-172

2.5184045435465955e-179

-2.2709498629311444e+153

-1.3123487377944479e+153

-1.5396067403637575e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	43	24
2	43	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1054×	body	2560	valid
254.0ms	5869×	body	80	valid
182.0ms	896×	body	1280	valid
121.0ms	2921×	body	80	nan
75.0ms	460×	body	640	valid
32.0ms	106×	body	5120	valid
26.0ms	219×	body	320	valid
8.0ms	106×	body	160	valid