Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
4.0ms	21×	body	2560	valid
3.0ms	23×	body	1280	valid
3.0ms	87×	body	80	nan
2.0ms	20×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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: 34.3b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

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:

17.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

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

prune309.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	173	10	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 8.2b

Counts

184 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

18.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	770	4550
1	3215	3424
2	5002	3236

prune313.0ms

Filtered

269 candidates to 110 candidates (40.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	267	2	269
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	270	9	279

Merged error: 8.1b

Counts

279 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

18.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5001	1940

prune263.0ms

Filtered

181 candidates to 95 candidates (52.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Merged error: 8.1b

Counts

190 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
5.6b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
19.0b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

91×	`prod-diff`
75×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
68×	`add-cube-cbrt` `log-prod` `exp-sum`
37×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`neg-mul-1` `add-log-exp`
7×	`pow1`
6×	`exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log` `log-pow` `difference-of-squares`
2×	`sub-neg` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `neg-log` `rem-exp-log`

Counts

4 → 178

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
71.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	535	4477
1	1473	2268
2	5002	2146

prune246.0ms

Filtered

190 candidates to 84 candidates (44.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	189	10	199

Merged error: 8.0b

Counts

199 → 10

regimes270.0ms

Accuracy

85.3% (3.9b remaining)

Error of 9.7b against oracle of 5.8b and baseline of 32.2b

bsearch108.0ms

Steps

Iters	Range	Point
7	6.184155830638016e+27	1.3306260697673677e+30	1.2919983862558445e+30
9	-2.7671842665178686e-160	-1.5330649496129563e-165	-5.079658430727619e-161
3	-5.857739979673282e+80	-4.162495233614184e+80	-4.862167828845928e+80

Iters

Range

Point

6.184155830638016e+27

1.3306260697673677e+30

1.2919983862558445e+30

-2.7671842665178686e-160

-1.5330649496129563e-165

-5.079658430727619e-161

-5.857739979673282e+80

-4.162495233614184e+80

-4.862167828845928e+80

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

sample988.0ms

Algorithm

intervals

Results

196.0ms	1040×	body	2560	valid
193.0ms	5867×	body	80	valid
137.0ms	899×	body	1280	valid
91.0ms	2906×	body	80	nan
52.0ms	436×	body	640	valid
34.0ms	115×	body	5120	valid
23.0ms	258×	body	320	valid
12.0ms	128×	body	160	valid