Details

sample293.0ms

Algorithm

intervals

Results

9.0ms	200×	body	80	valid
7.0ms	30×	body	2560	valid
6.0ms	104×	body	80	nan
5.0ms	24×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

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

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: 34.5b

Counts

2 → 1

localize12.0ms

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))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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:

23.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune236.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 6.5b

Counts

104 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`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 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
14.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
148.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
183.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune453.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Merged error: 6.3b

Counts

209 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.9b	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite985.0ms

Algorithm

rewrite-expression-head

Rules

15078×	`times-frac`
9183×	`add-sqr-sqrt`
7371×	`*-un-lft-identity`
6341×	`sqrt-prod`
5561×	`add-cube-cbrt`
1810×	`difference-of-squares`
986×	`associate-/l*`
905×	`distribute-lft-out--`
190×	`div-inv`
56×	`associate-/r/`
27×	`add-exp-log` `add-cbrt-cube`
16×	`cbrt-undiv` `div-exp`
14×	`sqrt-div`
12×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`pow1`
4×	`add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 4612

Calls

4 calls:

52.0ms	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
191.0ms	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
129.0ms	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Algorithm

egg-herbie

Counts

4624 → 4624

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5001	157498

prune10.3s

Filtered

4624 candidates to 2187 candidates (47.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	4623	1	4624
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	4624	9	4633

Merged error: 6.3b

Counts

4633 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
16.5b	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
9×	`add-cube-cbrt`
8×	`pow1` `log-prod` `exp-sum`
6×	`exp-prod` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-pow1` `pow1/2` `log-pow` `difference-of-squares`
2×	`rem-sqrt-square` `log-div` `exp-diff`
1×	`sub-neg` `diff-log` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 68

Calls

4 calls:

6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
70.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	234	599
1	644	550
2	1885	528
3	5001	514

prune254.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	80	9	89

Merged error: 6.3b

Counts

89 → 9

regimes222.0ms

Accuracy

87.5% (3.3b remaining)

Error of 9.3b against oracle of 5.9b and baseline of 32.7b

bsearch131.0ms

Steps

Iters	Range		Point
6	6.333441064762502e+69	2.6854631551896503e+70	2.6627070202833933e+70
9	6.38437193350804e-207	1.0453187696585907e-198	6.54999720168097e-207
7	-1.4866309009530871e+23	-7.041318958472561e+21	-1.0748567715632585e+22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample1.2s

Algorithm

intervals

Results

262.0ms	1082×	body	2560	valid
251.0ms	5823×	body	80	valid
183.0ms	889×	body	1280	valid
117.0ms	2907×	body	80	nan
70.0ms	442×	body	640	valid
34.0ms	107×	body	5120	valid
32.0ms	239×	body	320	valid
10.0ms	120×	body	160	valid