Details

Time bar (total: 5.0s)

sample273.0ms

Algorithm
intervals
Results
7.0ms186×body80valid
6.0ms34×body2560valid
4.0ms25×body1280valid
3.0ms88×body80nan
2.0ms14×body640valid
1.0ms13×body320valid
0.0ms2×body5120valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune5.0ms

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)
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

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:
47.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0368965
11241910
25001901

prune252.0ms

Filtered
103 candidates to 72 candidates (69.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
4.4b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.1b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×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 → 184
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
28.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
156.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
190.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07252897
132102743
250032723

prune490.0ms

Filtered
196 candidates to 144 candidates (73.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
1.9b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.4b
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
119×add-sqr-sqrt
94×*-un-lft-identity
70×add-cube-cbrt
32×add-exp-log
25×associate-/r*
24×difference-of-squares
23×add-cbrt-cube
16×div-exp
15×sqrt-prod
12×distribute-lft-out--
10×cbrt-undiv
6×prod-exp div-inv add-log-exp
5×pow1
4×associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ associate-/r/ associate-/l/
Counts
4 → 162
Calls
4 calls:
5.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
18.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
170.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
138.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07732158
135911999
250021976

prune411.0ms

Filtered
174 candidates to 118 candidates (67.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg distribute-rgt-neg-in 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 → 89
Calls
4 calls:
51.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
15.0ms
(- (- 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)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0428882
11811791
25001773

prune216.0ms

Filtered
101 candidates to 71 candidates (70.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.7b

regimes293.0ms

Accuracy

82.1% (4.7b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 31.9b

bsearch75.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
2.4992282662840617e+84
9
-6.219842315709727e-116
-4.3103875869831393e-125
-4.4270058556435274e-117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03415
13615
23615

end0.0ms

sample978.0ms

Algorithm
intervals
Results
209.0ms1092×body2560valid
195.0ms5868×body80valid
136.0ms894×body1280valid
90.0ms2861×body80nan
53.0ms439×body640valid
25.0ms106×body5120valid
22.0ms213×body320valid
7.0ms114×body160valid