Details

Time bar (total: 4.8s)

sample289.0ms

Algorithm
intervals
Results
8.0ms194×body80valid
8.0ms40×body2560valid
4.0ms28×body1280valid
2.0ms76×body80nan
1.0ms10×body640valid
0.0ms2×body5120valid
0.0ms3×body320valid
0.0ms1×body160valid

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: 34.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b
(- (* b_2 b_2) (* a c))
24.8b
(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:
44.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(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)
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0389850
11366779
25001753

prune298.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b
(- (* b_2 b_2) (* a c))
24.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
24×add-sqr-sqrt
16×add-cube-cbrt
13×add-exp-log associate-*r*
11×times-frac
10×fma-def add-log-exp
9×add-cbrt-cube
7×pow1
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ sqrt-prod flip-+ unswap-sqr
2×frac-times flip3-- sqrt-div div-exp associate-*l/ sum-log flip-- cbrt-unprod
1×cbrt-undiv +-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 fma-neg diff-log 1-exp associate-*r/ prod-diff pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 104
Calls
4 calls:
48.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
14.0ms
(+ (- 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)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0479897
12066778
25003729

prune293.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (* b_2 b_2) (* a c))
24.8b
(sqrt (- (* b_2 b_2) (* a c)))
24.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
3.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series188.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* b_2 b_2) (* a c))
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0159438
1511412
21701404
35002394

prune265.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.3b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.5b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

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:
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
29.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms
(/ (/ (+ 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)))))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify138.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
09195581
139124508
250014505

prune556.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

regimes181.0ms

Accuracy

89.9% (2.9b remaining)

Error of 8.6b against oracle of 5.7b and baseline of 34.3b

bsearch161.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.9445121160133635e+45
10
8.653734362945753e-196
5.147670875442886e-182
3.011407063919938e-189
11
-1.829086240692416e+154
-2.187052964502477e+134
-1.0524969308880696e+141

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample984.0ms

Algorithm
intervals
Results
212.0ms1107×body2560valid
195.0ms5865×body80valid
137.0ms908×body1280valid
90.0ms2861×body80nan
50.0ms422×body640valid
27.0ms97×body5120valid
19.0ms216×body320valid
7.0ms117×body160valid