Details

Time bar (total: 6.2s)

sample302.0ms

Algorithm
intervals
Results
15.0ms47×body2560valid
11.0ms167×body80valid
8.0ms32×body1280valid
8.0ms107×body80nan
3.0ms16×body640valid
2.0ms4×body5120valid
1.0ms9×body320valid
1.0ms6×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: 34.8b

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 b_2) (* a c))
1.6b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

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:
41.0ms
(/ (+ (- 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))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0358790
11261727
25001705

prune231.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
4.6b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.3b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite87.0ms

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)
28.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
138.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
164.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07293368
133203193
250013167

prune471.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.3b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.6b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
585×add-sqr-sqrt
584×*-un-lft-identity
392×add-cube-cbrt
96×distribute-lft-out-- difference-of-squares
83×associate-/l*
51×sqrt-prod
48×distribute-rgt-neg-in
28×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 → 485
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
54.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
176.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
150.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
015368628
150017983

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
75×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
25×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×add-cbrt-cube
7×div-exp
6×pow1
5×div-inv
3×cbrt-undiv flip3-- diff-log flip-- 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 associate-/r/ inv-pow
Counts
4 → 169
Calls
4 calls:
26.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
64.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms
(- (* b_2 b_2) (* a c))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06212277
126542085
250011944

prune237.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

regimes194.0ms

Accuracy

80.7% (4.6b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 29.2b

bsearch178.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
4.251985016727572e+125
7
-2.4269014694578893e-123
-3.257547761252762e-125
-2.3901106171036543e-123
8
-216491430331.63748
-6461629.042770713
-450366840.86426544
7
-2.3860448187824777e+68
-1.0929352752278947e+66
-3.0933810930860765e+67

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05035
15035

end0.0ms

sample1.6s

Algorithm
intervals
Results
365.0ms5748×body80valid
352.0ms1108×body2560valid
240.0ms933×body1280valid
166.0ms2801×body80nan
99.0ms476×body640valid
40.0ms106×body5120valid
37.0ms213×body320valid
13.0ms117×body160valid