Details

Time bar (total: 5.0s)

sample277.0ms

Algorithm
intervals
Results
8.0ms34×body2560valid
6.0ms188×body80valid
5.0ms30×body1280valid
3.0ms104×body80nan
2.0ms14×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms4×body160valid

simplify13.0ms

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: 33.5b

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) (sqrt (- (* b_2 b_2) (* a c))))
0.8b
(- (* b_2 b_2) (* a c))
20.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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:
10.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(+ (- 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)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0358790
11261727
25001705

prune237.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.1b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
158×add-sqr-sqrt
157×*-un-lft-identity
89×add-cube-cbrt
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
20×sqrt-prod
17×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 206
Calls
4 calls:
8.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
137.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
163.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07413477
133293295
250013269

prune504.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.7b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
20.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
32×add-exp-log
28×associate-/r*
26×distribute-lft-out-- difference-of-squares
23×add-cbrt-cube
16×div-exp sqrt-prod
13×distribute-rgt-neg-in
10×cbrt-undiv
8×add-log-exp
6×prod-exp div-inv
5×pow1
4×associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log associate-/r/ associate-/l/
Counts
4 → 180
Calls
4 calls:
8.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
18.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
174.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
147.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08142582
137872402
250012379

prune428.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.8b
(- (* b_2 b_2) (* a c))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

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:
13.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
31.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06212277
126542085
250011944

prune258.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

regimes162.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.6b

bsearch146.0ms

Steps
ItersRangePoint
9
1.846147638884188e+104
1.7844061428947563e+109
4.3957752798560445e+108
8
-1.0308405028667604e-278
-9.93812268464695e-282
-1.2249666784418393e-279
9
-3.3506371122085595e+158
-5.17073721832495e+150
-9.268713688859225e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04633
14833
24833

end0.0ms

sample1.0s

Algorithm
intervals
Results
222.0ms1107×body2560valid
198.0ms5877×body80valid
135.0ms876×body1280valid
92.0ms2996×body80nan
53.0ms420×body640valid
28.0ms119×body5120valid
22.0ms236×body320valid
8.0ms125×body160valid