Details

Time bar (total: 7.7s)

sample284.0ms

Algorithm
intervals
Results
8.0ms181×body80valid
7.0ms32×body2560valid
6.0ms36×body1280valid
4.0ms111×body80nan
1.0ms10×body640valid
1.0ms12×body320valid
1.0ms3×body5120valid
0.0ms2×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: 36.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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:
10.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune313.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
3.8b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

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:
4.0ms
(- (* b_2 b_2) (* a c))
20.0ms
(/ (/ (+ 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)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* b_2 b_2) (* a c))
138.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
167.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07613434
134903258
250023250

prune517.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
2.5b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.8b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

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:
4.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
28.0ms
(/ (/ 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:
37.0ms
(- (* b_2 b_2) (* a c))
180.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
148.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015618690
150018042

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (/ 1 1)) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
3761×times-frac
1996×add-sqr-sqrt
1995×*-un-lft-identity
1451×add-cube-cbrt
272×distribute-lft-out-- difference-of-squares
169×sqrt-prod
157×distribute-rgt-neg-in
150×div-inv
122×add-exp-log
118×div-exp
61×prod-diff
44×1-exp associate-/l*
27×associate-/r/
26×rec-exp
25×associate-/r* add-cbrt-cube
21×distribute-lft-neg-in
15×cbrt-undiv
11×fma-neg
10×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
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 → 1356
Calls
4 calls:
48.0ms
(/ (/ 1 (/ 1 1)) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
11.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (/ 1 (/ 1 1)) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify298.0ms

Algorithm
egg-herbie
Counts
1368 → 1368
Iterations

Useful iterations: 1 (63.0ms)

IterNodesCost
0490127268
1500227009

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.4b

regimes318.0ms

Accuracy

92% (1.9b remaining)

Error of 7.5b against oracle of 5.6b and baseline of 29.2b

bsearch145.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
2445759453.473797
11
-2.9129801656201065e-276
-1.2526982634953812e-296
-3.896155291582558e-285
9
-3.2701742958179892e+66
-3.862137329617324e+60
-1.0461303908572575e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04323
14323

end0.0ms

sample1.1s

Algorithm
intervals
Results
236.0ms1098×body2560valid
212.0ms5841×body80valid
163.0ms933×body1280valid
101.0ms2922×body80nan
59.0ms450×body640valid
26.0ms101×body5120valid
23.0ms233×body320valid
7.0ms101×body160valid