Details

Time bar (total: 8.3s)

sample312.0ms

Algorithm
intervals
Results
18.0ms185×body80valid
12.0ms30×body2560valid
8.0ms25×body1280valid
8.0ms99×body80nan
5.0ms20×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
34.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0358790
11261727
25001705

prune238.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
3.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.2b
(/ (+ 0 (* a c)) (- (- 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
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* 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 → 200
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
29.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
139.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
166.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07293368
133203193
250013167

prune497.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
2.3b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.4b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1827×add-sqr-sqrt
1826×*-un-lft-identity
1346×add-cube-cbrt
267×associate-/l*
240×distribute-lft-out-- difference-of-squares
123×sqrt-prod
120×distribute-rgt-neg-in
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 → 1142
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
107.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
90.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
106.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify261.0ms

Algorithm
egg-herbie
Counts
1154 → 1154
Iterations

Useful iterations: 1 (68.0ms)

IterNodesCost
0424224730
1500124067

prune2.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1
5×associate-*l*
4×prod-exp distribute-lft-out
3×flip3-+ sqrt-prod flip-+ unswap-sqr
2×frac-times flip3-- distribute-rgt-neg-in sqrt-div div-exp associate-*l/ sum-log flip-- cbrt-unprod
1×cbrt-undiv +-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 84
Calls
4 calls:
51.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
2.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
36.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0448824
11956724
25002684

prune223.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.6b

regimes193.0ms

Accuracy

88.6% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 32.4b

bsearch326.0ms

Steps
ItersRangePoint
7
6.714891876596302e+121
1.686395921989292e+123
2.292661527341346e+122
6
2.4634856426385367e+30
1.375897298344625e+31
4.6383712677255495e+30
11
1.7382738099505427e-22
0.7032085127721847
0.023173574830720484
10
-5.399505147647774e-194
-1.4984247517127078e-204
-1.5120874391809866e-204
8
-2.1136969993533704e+133
-9.628024177185589e+129
-2.1419401754731713e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05637
15837
25837

end0.0ms

sample2.0s

Algorithm
intervals
Results
504.0ms5896×body80valid
428.0ms1085×body2560valid
292.0ms893×body1280valid
228.0ms2929×body80nan
116.0ms442×body640valid
54.0ms117×body5120valid
46.0ms226×body320valid
16.0ms98×body160valid