Details

Time bar (total: 6.9s)

sample310.0ms

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

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize12.0ms

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)))

rewrite67.0ms

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:
32.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0389850
11366779
25001753

prune291.0ms

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)))

rewrite86.0ms

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 expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
39.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
25.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
141.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
169.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
07613434
134903258
250023250

prune507.0ms

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))
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)))

rewrite124.0ms

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/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/l/
Counts
4 → 495
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
27.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
53.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
180.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
153.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015618691
150028043

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

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
44×add-exp-log
43×div-inv
32×div-exp
29×associate-/r/
27×associate-/l*
21×distribute-lft-neg-in
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/r*
11×fma-neg
10×add-log-exp
8×cbrt-undiv rec-exp 1-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 → 548
Calls
4 calls:
43.0ms
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0196311056
150019439

prune675.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

regimes186.0ms

Accuracy

94.2% (1.4b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.2b

bsearch117.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
3.6708609126801744e+125
4
-1.3699538778299852e-160
-8.754296253605712e-161
-8.908835082502404e-161
7
-2.3860448187824777e+68
-1.0929352752278947e+66
-2.3202538172935113e+68

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14224

end0.0ms

sample1.6s

Algorithm
intervals
Results
376.0ms5748×body80valid
353.0ms1108×body2560valid
242.0ms933×body1280valid
165.0ms2801×body80nan
99.0ms476×body640valid
40.0ms106×body5120valid
33.0ms213×body320valid
13.0ms117×body160valid