Details

Time bar (total: 11.3s)

sample293.0ms

Algorithm
intervals
Results
7.0ms36×body2560valid
6.0ms187×body80valid
4.0ms76×body80nan
4.0ms22×body1280valid
1.0ms5×body5120valid
1.0ms9×body640valid
1.0ms9×body320valid
0.0ms4×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize11.0ms

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))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
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 → 91
Calls
4 calls:
10.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (- 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:
83.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0368965
11241910
25001901

prune248.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.2b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 187
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
151.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
186.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07302960
132002803
250012783

prune486.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.3b
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
5.2b
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
3063×times-frac
1689×add-sqr-sqrt
1446×*-un-lft-identity
1204×add-cube-cbrt
242×difference-of-squares
237×associate-/l*
124×sqrt-prod
121×distribute-lft-out--
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×associate-/r/
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 1025
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
58.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
99.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify236.0ms

Algorithm
egg-herbie
Counts
1037 → 1037
Iterations

Useful iterations: 1 (65.0ms)

IterNodesCost
0425921067
1500120479

prune2.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

localize16.0ms

Local error

Found 4 expressions with local error:

2.3b
(/ (/ (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a) c)
4.2b
(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
5.2b
(/ (/ 1 (/ (/ (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a) c)) a)
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
4341×times-frac
2237×add-sqr-sqrt
1994×*-un-lft-identity
1752×add-cube-cbrt
726×log-prod exp-sum
327×associate-/l*
242×difference-of-squares
124×sqrt-prod
121×distribute-lft-out--
58×div-inv
37×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×pow1 associate-/r*
4×exp-prod associate-/r/ add-log-exp
3×rec-exp 1-exp
2×log-div flip3-- frac-2neg exp-diff sqrt-div clear-num flip-- associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 log-pow rem-exp-log
Counts
4 → 1389
Calls
4 calls:
16.0ms
(/ (/ (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a) c)
9.0ms
(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
74.0ms
(/ (/ 1 (/ (/ (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (/ (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a) c)
72.0ms
(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
96.0ms
(/ (/ 1 (/ (/ (exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a) c)) a)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify292.0ms

Algorithm
egg-herbie
Counts
1401 → 1401
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0500232147

prune4.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

regimes229.0ms

Accuracy

82.7% (4.6b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 32.3b

bsearch76.0ms

Steps
ItersRangePoint
6
1.7071993853452014e+98
1.0593861995340862e+99
1.0479007947857462e+99
8
-2.0898868129100636e-78
-1.06178241226232e-82
-4.653701756906352e-82

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03315
13315

end0.0ms

sample1.0s

Algorithm
intervals
Results
212.0ms1069×body2560valid
199.0ms5770×body80valid
147.0ms923×body1280valid
88.0ms2853×body80nan
58.0ms463×body640valid
35.0ms127×body5120valid
21.0ms227×body320valid
8.0ms131×body160valid