Details

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

12.0ms	44×	body	2560	valid
8.0ms	159×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	21×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	5×	body	80	invalid

simplify370.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune5.0ms

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: 35.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune146.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 5.6b

Counts

104 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
4.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
54.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune227.0ms

Filtered

144 candidates to 196 candidates (-36.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	198	9	207

Merged error: 5.6b

Counts

207 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
2.1b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.2b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
25.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
53.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
43.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1530	7327
1	5001	6764

prune299.0ms

Filtered

297 candidates to 449 candidates (-51.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	449	9	458

Merged error: 5.6b

Counts

458 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `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` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

10.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	586	1942
1	2438	1777
2	5001	1652

prune92.0ms

Filtered

80 candidates to 166 candidates (-107.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	6	7
Picked	1	0	1
Done	1	0	1
Total	168	7	175

Merged error: 5.6b

Counts

175 → 7

regimes268.0ms

Accuracy

96% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.9b

bsearch90.0ms

Steps

Iters	Range	Point
8	6.937658602873116e+85	3.055994355226437e+88	1.824521137991738e+88
7	2.0534282030563515e-210	1.361119887994178e-208	2.0893600825100673e-210
7	-9.892024451400646e+155	-6.981222205078894e+153	-1.0147090346057053e+154

Iters

Range

Point

6.937658602873116e+85

3.055994355226437e+88

1.824521137991738e+88

2.0534282030563515e-210

1.361119887994178e-208

2.0893600825100673e-210

-9.892024451400646e+155

-6.981222205078894e+153

-1.0147090346057053e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	19
1	40	19
2	40	19

end0.0ms

sample2.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

266.0ms	1069×	body	2560	valid
232.0ms	5205×	body	80	valid
175.0ms	865×	body	1280	valid
65.0ms	404×	body	640	valid
35.0ms	118×	body	5120	valid
26.0ms	218×	body	320	valid
21.0ms	502×	body	80	nan
10.0ms	121×	body	160	valid
8.0ms	185×	body	80	invalid

Details

sample2.1s

simplify370.0ms

prune5.0ms

localize12.0ms

rewrite31.0ms

series74.0ms

simplify42.0ms

prune146.0ms

localize10.0ms

rewrite40.0ms

series118.0ms

simplify100.0ms

prune227.0ms

localize11.0ms

rewrite76.0ms

series115.0ms

simplify91.0ms

prune299.0ms

localize9.0ms

rewrite31.0ms

series56.0ms

simplify67.0ms

prune92.0ms

regimes268.0ms

bsearch90.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling