Details

Time bar (total: 5.0s)

sample292.0ms

Algorithm
intervals
Results
8.0ms42×body2560valid
8.0ms191×body80valid
3.0ms20×body1280valid
3.0ms96×body80nan
2.0ms17×body640valid
1.0ms4×body5120valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

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:
28.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (* b_2 b_2) (* a c))
76.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05493055
118262150
250022063

prune352.0ms

Filtered
183 candidates to 97 candidates (53.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b
(- (* b_2 b_2) (* a c))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(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:
15.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
7.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
37.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (- b_2) (sqrt (- (* 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 (56.0ms)

IterNodesCost
06092985
123341993
250021940

prune315.0ms

Filtered
181 candidates to 96 candidates (53.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b
(- (* b_2 b_2) (* a c))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

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:
15.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
37.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07704550
132153424
250023236

prune369.0ms

Filtered
269 candidates to 112 candidates (41.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b
(- (* b_2 b_2) (* a c))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
569×add-sqr-sqrt
568×*-un-lft-identity
396×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
61×prod-diff
44×add-exp-log
43×div-inv
32×div-exp
29×associate-/r/
27×associate-/r*
21×distribute-lft-neg-in
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/l*
11×fma-neg
10×add-log-exp
8×cbrt-undiv rec-exp 1-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 548
Calls
4 calls:
23.0ms
(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify122.0ms

Algorithm
egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0188710995
150019278

prune697.0ms

Filtered
560 candidates to 200 candidates (35.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

regimes188.0ms

Accuracy

81% (5.4b remaining)

Error of 11.2b against oracle of 5.8b and baseline of 34.3b

bsearch84.0ms

Steps
ItersRangePoint
7
9.786063674806627e+75
3.1345211132670796e+77
2.9083064714494895e+77
9
-6.944152938449299e-155
-2.632619076242731e-163
-6.842303289862193e-155

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03416
13416

end0.0ms

sample1.0s

Algorithm
intervals
Results
215.0ms1080×body2560valid
199.0ms5913×body80valid
144.0ms915×body1280valid
96.0ms2980×body80nan
49.0ms398×body640valid
28.0ms114×body5120valid
24.0ms212×body320valid
6.0ms95×body160valid