Details

Time bar (total: 5.3s)

sample300.0ms

Algorithm
intervals
Results
8.0ms184×body80valid
6.0ms34×body1280valid
5.0ms25×body2560valid
4.0ms115×body80nan
2.0ms9×body5120valid
2.0ms15×body640valid
1.0ms10×body320valid
0.0ms5×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: 35.9b

localize12.0ms

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))
1.7b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

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:
74.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms
(- (* b_2 b_2) (* a c))
31.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0358790
11261727
25001705

prune232.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.5b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite208.0ms

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:
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
64.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
129.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
154.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
53.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07413477
133293295
250013269

prune492.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.8b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.5b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite144.0ms

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:
27.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
44.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
163.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
137.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08142582
137872402
250012379

prune406.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
0.4b
(- (* b_2 b_2) (* a c))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×add-exp-log
26×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
17×div-exp
13×add-cbrt-cube
10×add-log-exp
7×1-exp associate-/r*
6×pow1 prod-exp
5×cbrt-undiv div-inv
4×rec-exp sqrt-prod
3×flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square pow-flip distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ cbrt-unprod inv-pow
Counts
4 → 104
Calls
4 calls:
54.0ms
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
9.0ms
(- (* b_2 b_2) (* a c))
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
29.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05211126
12188976
25002931

prune186.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes140.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.4b

bsearch134.0ms

Steps
ItersRangePoint
9
1.7695728335377845e+74
3.738006738925262e+80
5.232488921342498e+79
11
-1.5799869936663156e-158
-6.164197719833672e-182
-6.278504568756145e-182
6
-3.413061301452514e+122
-2.3517657564579724e+121
-1.5254699676315931e+122

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04324
14524
24524

end0.0ms

sample1.2s

Algorithm
intervals
Results
232.0ms1059×body2560valid
214.0ms5785×body80valid
153.0ms896×body1280valid
100.0ms2930×body80nan
68.0ms490×body640valid
31.0ms115×body5120valid
23.0ms228×body320valid
8.0ms122×body160valid