Details

Time bar (total: 19.9s)

sample346.0ms

Algorithm
intervals
Results
7.0ms182×body80valid
5.0ms28×body2560valid
4.0ms29×body1280valid
3.0ms89×body80nan
2.0ms22×body640valid
1.0ms5×body5120valid
0.0ms8×body160valid
0.0ms1×body320valid

simplify36.0ms

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: 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 b_2) (* a c))
1.8b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite121.0ms

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:
69.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
24.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(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

prune299.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite199.0ms

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:
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
57.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
151.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
175.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
09195579
139184508
250014505

prune576.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.0b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1872×add-sqr-sqrt
1871×*-un-lft-identity
1387×add-cube-cbrt
267×associate-/l*
242×distribute-lft-out-- difference-of-squares
154×sqrt-prod
142×distribute-rgt-neg-in
60×prod-diff
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
21×distribute-lft-neg-in
13×cbrt-undiv
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1226
Calls
4 calls:
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
71.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
146.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
96.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
116.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify266.0ms

Algorithm
egg-herbie
Counts
1238 → 1238
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0446326936
1500225697

prune2.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b_2 b_2) (* a c))
1.0b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite814.0ms

Algorithm
rewrite-expression-head
Rules
11112×times-frac
5738×add-sqr-sqrt
5737×*-un-lft-identity
4221×add-cube-cbrt
2619×cbrt-prod
758×distribute-lft-out-- difference-of-squares
431×associate-/l*
412×sqrt-prod
400×distribute-rgt-neg-in
92×div-inv
61×prod-diff
36×add-exp-log
25×div-exp
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×cbrt-undiv add-log-exp
7×neg-mul-1 associate-/r/
6×associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×rec-exp flip3-- diff-log 1-exp 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 → 3173
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* a c))
240.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
122.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify678.0ms

Algorithm
egg-herbie
Counts
3185 → 3185
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0500190576

prune10.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes182.0ms

Accuracy

93.8% (1.5b remaining)

Error of 7.0b against oracle of 5.4b and baseline of 30.6b

bsearch154.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
9.766388217822194e+89
9
-1.9057533827392632e-295
-5.303124627677042e-305
-1.1959062841727918e-304
10
-7.651517840437919e+135
-3.890563902308465e+123
-4.739386840053889e+131

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05137
15137

end0.0ms

sample1.0s

Algorithm
intervals
Results
188.0ms1056×body2560valid
186.0ms5792×body80valid
135.0ms938×body1280valid
89.0ms2914×body80nan
53.0ms455×body640valid
25.0ms103×body5120valid
19.0ms225×body320valid
6.0ms108×body160valid