Details

analyze618.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample42.0ms

Algorithm

intervals

Results

10.0ms	39×	body	2560	valid
7.0ms	167×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	17×	body	640	valid
1.0ms	31×	body	80	nan
1.0ms	7×	body	320	valid
0.0ms	10×	body	80	invalid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify495.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

9.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
35.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5743	1403

prune139.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 6.2b

Counts

95 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
2.1b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`div-inv` `distribute-lft-out` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
54.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4932	2261
1	4932	2261

prune133.0ms

Filtered

96 candidates to 125 candidates (-30.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	127	7	134

Merged error: 6.1b

Counts

134 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

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 → 160

Calls

4 calls:

13.0ms	(/ 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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4972	3316
1	4972	3316

prune145.0ms

Filtered

102 candidates to 172 candidates (-68.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	171	8	179

Merged error: 6.1b

Counts

179 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
6.0b	(/ (neg c) (* a (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
11.7b	(* a (/ (neg c) (* a (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`times-frac`
19×	`add-sqr-sqrt`
18×	`add-exp-log` `add-cbrt-cube`
16×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`associate-/l*`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-*r/` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r/`
3×	`neg-mul-1` `associate-l` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `distribute-frac-neg` `flip--` `flip-+` `div-inv`
1×	`neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `distribute-rgt-neg-out` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (neg c) (* a (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(* a (/ (neg c) (* a (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(/ (neg c) (* a (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
42.0ms	(* a (/ (neg c) (* a (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4950	1457
1	4950	1457

prune98.0ms

Filtered

87 candidates to 114 candidates (-31.0%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	114	8	122

Merged error: 6.1b

Counts

122 → 8

regimes280.0ms

Accuracy

88.4% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 33.1b

bsearch82.0ms

Steps

Iters	Range		Point
10	104417167155448.2	2.5578988625229126e+26	7.210670058365327e+25
7	7.330608843598135e-234	8.44883353063025e-232	2.517728687625501e-233
8	-3.530573512040272e+132	-5.787950309246652e+129	-2.3941494279877027e+132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	59
1	88	59

end0.0ms

sample1.1s

Algorithm

intervals

Results

281.0ms	1109×	body	2560	valid
229.0ms	5118×	body	80	valid
181.0ms	857×	body	1280	valid
75.0ms	462×	body	640	valid
39.0ms	115×	body	5120	valid
30.0ms	736×	body	80	nan
27.0ms	227×	body	320	valid
11.0ms	248×	body	80	invalid
9.0ms	112×	body	160	valid

Details

analyze618.0ms

sample42.0ms

simplify495.0ms

prune12.0ms

localize11.0ms

rewrite30.0ms

series77.0ms

simplify54.0ms

prune139.0ms

localize12.0ms

rewrite31.0ms

series113.0ms

simplify68.0ms

prune133.0ms

localize10.0ms

rewrite36.0ms

series67.0ms

simplify66.0ms

prune145.0ms

localize12.0ms

rewrite33.0ms

series119.0ms

simplify57.0ms

prune98.0ms

regimes280.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling