Details

Time bar (total: 6.9s)

sample67.0ms

Algorithm
intervals
Results
16.0ms188×body80valid
13.0ms32×body2560valid
9.0ms91×body80nan
8.0ms25×body1280valid
5.0ms18×body640valid
3.0ms6×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize9.0ms

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))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

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:
33.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0368965
11241910
25001901

prune228.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.2b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.5b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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:
18.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
24.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
148.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
181.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07302960
132002803
250012783

prune516.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.6b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.2b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
831×times-frac
549×add-sqr-sqrt
450×*-un-lft-identity
352×add-cube-cbrt
98×difference-of-squares
74×associate-/l*
52×sqrt-prod
49×distribute-lft-out--
25×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 440
Calls
4 calls:
20.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
46.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
159.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
128.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
452 → 452
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015717388
150016820

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.3b
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
9.5b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt
52×times-frac
51×*-un-lft-identity
33×add-cube-cbrt
28×add-exp-log
24×associate-*l*
18×add-cbrt-cube
16×difference-of-squares
13×associate-*r*
11×sqrt-prod
9×div-exp
8×prod-exp distribute-lft-out--
7×pow1
6×associate-/r* add-log-exp unswap-sqr
5×cbrt-undiv
4×flip3-- associate-/r/ flip-- cbrt-unprod
3×div-inv associate-/l*
2×rec-exp sqrt-div 1-exp associate-/l/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 141
Calls
4 calls:
17.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
24.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
151.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
184.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07001778
132081574
250011556

prune351.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.0b

regimes251.0ms

Accuracy

88.7% (2.9b remaining)

Error of 8.5b against oracle of 5.6b and baseline of 31.3b

bsearch183.0ms

Steps
ItersRangePoint
8
5.408584085660923e+89
1.6744273082514658e+93
2.8046284917653458e+91
9
8.576105435740817e-275
2.0823221738669132e-266
1.4667701057073822e-270
9
-2.7053725391627148e-24
-2.8797342925733515e-30
-2.7641518967124233e-27

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03622
13622

end0.0ms

sample2.0s

Algorithm
intervals
Results
491.0ms5789×body80valid
424.0ms1042×body2560valid
303.0ms918×body1280valid
221.0ms2837×body80nan
131.0ms481×body640valid
51.0ms107×body5120valid
51.0ms250×body320valid
17.0ms108×body160valid