Details

Time bar (total: 4.4s)

sample36.0ms

Algorithm
intervals
Results
6.0ms33×body2560valid
6.0ms193×body80valid
5.0ms30×body1280valid
3.0ms102×body80nan
1.0ms6×body5120valid
1.0ms9×body640valid
0.0ms5×body320valid
0.0ms4×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(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:
41.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05493055
118262150
250022063

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

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:
28.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
34.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07704550
132153424
250023236

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

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:
43.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05493055
118262150
250022063

prune314.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

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:
61.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
35.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
09067442
132894548
250014309

prune315.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

regimes220.0ms

Accuracy

82.3% (5.0b remaining)

Error of 10.8b against oracle of 5.8b and baseline of 33.9b

bsearch83.0ms

Steps
ItersRangePoint
7
7.8930669794294e+68
1.794276654474529e+70
1.7701741483501238e+70
9
-1.8496456666423901e-16
-6.821017948976997e-23
-6.931537337855704e-23

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03213
13613
23613

end0.0ms

sample1.0s

Algorithm
intervals
Results
219.0ms1059×body2560valid
199.0ms5874×body80valid
146.0ms884×body1280valid
88.0ms2865×body80nan
59.0ms448×body640valid
35.0ms117×body5120valid
20.0ms208×body320valid
8.0ms126×body160valid