Details

Time bar (total: 7.8s)

sample300.0ms

Algorithm
intervals
Results
13.0ms43×body2560valid
13.0ms181×body80valid
10.0ms40×body1280valid
5.0ms79×body80nan
3.0ms12×body640valid
1.0ms3×body5120valid
0.0ms3×body320valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
21.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
13.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune308.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
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 → 284
Calls
4 calls:
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
137.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
09195579
139184508
250014505

prune586.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
630×add-sqr-sqrt
629×*-un-lft-identity
433×add-cube-cbrt
98×distribute-lft-out-- difference-of-squares
83×associate-/l*
82×sqrt-prod
70×distribute-rgt-neg-in
60×prod-diff
28×associate-/r*
22×div-inv
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
9×cbrt-undiv div-exp
8×add-log-exp
7×neg-mul-1
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
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 neg-log associate-/l/
Counts
4 → 569
Calls
4 calls:
26.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
154.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
581 → 581
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0175510833
150019431

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
2.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.9b
(/ (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ a c))
21.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
569×add-sqr-sqrt
568×*-un-lft-identity
396×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
61×prod-diff
43×div-inv
29×associate-/r/
27×associate-/l*
21×distribute-lft-neg-in
17×flip3-- flip--
16×add-exp-log add-cbrt-cube
13×associate-/r*
11×fma-neg
10×add-log-exp
8×cbrt-undiv div-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 536
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms
(/ (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ a c))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
155.0ms
(/ (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ a c))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify122.0ms

Algorithm
egg-herbie
Counts
548 → 548
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0210011010
150019830

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.3b

regimes178.0ms

Accuracy

93.6% (1.5b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.6b

bsearch155.0ms

Steps
ItersRangePoint
9
1.0966316111626227e+109
8.247031634266059e+117
1.6719249902234693e+111
6
-6.029898348274424e-278
-1.071274884863318e-278
-1.0853211705499398e-278
7
-1.347931383778874e+29
-1.5320971041566743e+27
-1.3279271689820989e+29

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04727
14927
24927

end0.0ms

sample1.6s

Algorithm
intervals
Results
381.0ms5823×body80valid
345.0ms1084×body2560valid
239.0ms904×body1280valid
175.0ms2979×body80nan
94.0ms455×body640valid
48.0ms113×body5120valid
35.0ms212×body320valid
12.0ms110×body160valid