Details

Time bar (total: 4.9s)

sample55.0ms

Algorithm
intervals
Results
16.0ms209×body80valid
12.0ms39×body2560valid
6.0ms107×body80nan
5.0ms21×body1280valid
2.0ms10×body640valid
1.0ms4×body320valid
0.0ms3×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: 32.2b

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))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

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:
45.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
5.0ms
(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)
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)))

simplify69.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05493055
118262150
250012063

prune333.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

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))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

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))))))
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
64.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms
(- (* b_2 b_2) (* a c))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07704550
132153424
250023236

prune364.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize10.0ms

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))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite77.0ms

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)
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(- (* 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)
64.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05493056
118142150
250022063

prune316.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize11.0ms

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))))
1.2b
(- (* b_2 b_2) (* a c))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

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:
51.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
20.0ms
(- (- 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)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms
(- (* b_2 b_2) (* a c))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06092985
123341993
250011940

prune311.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

regimes203.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.1b

bsearch82.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
6.771165814787109e+125
7
-2.4269014694578893e-123
-3.257547761252762e-125
-2.3165289123951838e-123

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03817
14417
24417

end0.0ms

sample1.6s

Algorithm
intervals
Results
385.0ms5956×body80valid
348.0ms1053×body2560valid
249.0ms905×body1280valid
172.0ms2823×body80nan
99.0ms447×body640valid
40.0ms102×body5120valid
32.0ms195×body320valid
12.0ms103×body160valid