Details

Time bar (total: 3.9s)

sample288.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
6.0ms38×body1280valid
6.0ms177×body80valid
3.0ms21×body640valid
2.0ms79×body80nan
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms7×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite90.0ms

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:
55.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(- (- 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:
82.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05493055
118262150
250022063

prune355.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune19.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite89.0ms

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:
57.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(- (- b_2) (sqrt (- (* 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)))) (/ 1 a))
32.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06092985
123341993
250021940

prune314.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(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:
30.0ms
(/ 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))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
35.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(- (- 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

prune344.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

regimes193.0ms

Accuracy

87.2% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 39.8b

bsearch68.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
5
-1.2023865605984147e-79
-5.347575839305805e-80
-8.364554704106616e-80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03415
13415

end0.0ms

sample1.0s

Algorithm
intervals
Results
204.0ms1075×body2560valid
196.0ms5860×body80valid
141.0ms904×body1280valid
92.0ms2862×body80nan
58.0ms457×body640valid
29.0ms114×body5120valid
19.0ms211×body320valid
7.0ms120×body160valid