Details

sample274.0ms

Algorithm

intervals

Results

6.0ms	35×	body	2560	valid
6.0ms	179×	body	80	valid
5.0ms	32×	body	1280	valid
4.0ms	89×	body	80	nan
2.0ms	15×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.3b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
54.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune353.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.3b	(/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`associate-/r*`
32×	`distribute-lft-out--` `difference-of-squares`
19×	`sqrt-prod`
17×	`add-exp-log`
16×	`distribute-rgt-neg-in`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
7×	`flip3--` `flip--`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `inv-pow`

Counts

4 → 214

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.0ms	(/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
168.0ms	(/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
37.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	633	2890
1	2948	2630
2	5001	2476

prune364.0ms

Filtered

226 candidates to 112 candidates (49.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.3b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune318.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.3b	(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

918×	`times-frac`
552×	`add-sqr-sqrt`
551×	`*-un-lft-identity`
367×	`add-cube-cbrt`
92×	`distribute-lft-out--` `difference-of-squares`
49×	`sqrt-prod`
48×	`add-exp-log`
46×	`distribute-rgt-neg-in`
44×	`div-inv`
34×	`div-exp` `associate-/r*`
31×	`associate-/r/`
18×	`add-cbrt-cube`
17×	`flip3--` `flip--`
16×	`associate-/l*`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 509

Calls

4 calls:

35.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
24.0ms	(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
89.0ms	(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
33.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

521 → 521

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1755	9353
1	5001	8419

prune680.0ms

Filtered

521 candidates to 194 candidates (37.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes245.0ms

Accuracy

85% (4.3b remaining)

Error of 9.6b against oracle of 5.3b and baseline of 34.1b

bsearch69.0ms

Steps

Iters	Range		Point
10	2.531505514381809e+64	2.4051897841780437e+82	2.3609763237480153e+82
3	-2.3762030729656124e-61	-1.6676843733113775e-61	-1.889096466953326e-61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	17
1	44	17
2	44	17

end0.0ms

sample959.0ms

Algorithm

intervals

Results

195.0ms	1047×	body	2560	valid
194.0ms	5916×	body	80	valid
132.0ms	897×	body	1280	valid
85.0ms	2837×	body	80	nan
49.0ms	419×	body	640	valid
31.0ms	133×	body	5120	valid
25.0ms	242×	body	320	valid
7.0ms	116×	body	160	valid