Details

Time bar (total: 19.1s)

sample345.0ms

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

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize13.0ms

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)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
67.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0358790
11261727
25001705

prune230.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

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)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
158×add-sqr-sqrt
157×*-un-lft-identity
89×add-cube-cbrt
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
20×sqrt-prod
17×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv div-exp
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 → 206
Calls
4 calls:
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
54.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
143.0ms
(/ (/ (+ 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)))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07413477
133293295
250013269

prune484.0ms

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)))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1831×add-sqr-sqrt
1830×*-un-lft-identity
1346×add-cube-cbrt
267×associate-/l*
242×distribute-lft-out-- difference-of-squares
124×sqrt-prod
121×distribute-rgt-neg-in
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
8×add-log-exp
6×associate-/r*
5×pow1
4×associate-/r/
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 → 1148
Calls
4 calls:
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
137.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
96.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
115.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify257.0ms

Algorithm
egg-herbie
Counts
1160 → 1160
Iterations

Useful iterations: 1 (67.0ms)

IterNodesCost
0428724836
1500124170

prune2.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize20.0ms

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)))

rewrite728.0ms

Algorithm
rewrite-expression-head
Rules
11112×times-frac
5697×add-sqr-sqrt
5696×*-un-lft-identity
4180×add-cube-cbrt
2619×cbrt-prod
758×distribute-lft-out-- difference-of-squares
431×associate-/l*
382×sqrt-prod
379×distribute-rgt-neg-in
92×div-inv
36×add-exp-log
25×div-exp
13×add-cbrt-cube
10×cbrt-undiv add-log-exp
7×associate-/r/
6×associate-/r*
5×pow1
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 → 3093
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
225.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify671.0ms

Algorithm
egg-herbie
Counts
3105 → 3105
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0500188462

prune10.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes178.0ms

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

sample1.1s

Algorithm
intervals
Results
187.0ms1056×body2560valid
187.0ms5792×body80valid
141.0ms938×body1280valid
83.0ms2914×body80nan
53.0ms455×body640valid
22.0ms103×body5120valid
19.0ms225×body320valid
6.0ms108×body160valid