Details

sample53.0ms

Algorithm

intervals

Results

13.0ms	200×	body	80	valid
7.0ms	21×	body	2560	valid
6.0ms	23×	body	1280	valid
5.0ms	87×	body	80	nan
4.0ms	5×	body	5120	valid
4.0ms	20×	body	640	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

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)))

rewrite75.0ms

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:

44.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (- 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)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (43.0ms)

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

prune329.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

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)))

rewrite66.0ms

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:

26.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
17.0ms	(- (- 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)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (63.0ms)

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

prune358.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize13.0ms

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)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
146×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`add-exp-log` `associate-l`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sqrt-div` `associate-*r/` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 292

Calls

4 calls:

62.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(- (- 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)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	906	7441
1	3295	4548
2	5001	4309

prune335.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.1b

localize18.0ms

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)))

rewrite44.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
22.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
70.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (37.0ms)

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

prune282.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.0b

regimes269.0ms

Accuracy

85.3% (3.9b remaining)

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

bsearch128.0ms

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	43	25
1	45	25
2	45	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

385.0ms	5867×	body	80	valid
337.0ms	1040×	body	2560	valid
239.0ms	899×	body	1280	valid
183.0ms	2906×	body	80	nan
93.0ms	436×	body	640	valid
45.0ms	258×	body	320	valid
44.0ms	115×	body	5120	valid
14.0ms	128×	body	160	valid