Details

Time bar (total: 35.2s)

sample289.0ms

Algorithm
intervals
Results
7.0ms177×body80valid
7.0ms38×body2560valid
4.0ms26×body1280valid
3.0ms112×body80nan
2.0ms20×body640valid
1.0ms6×body5120valid
1.0ms9×body320valid
0.0ms4×body160valid

simplify13.0ms

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: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.7b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

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:
41.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
2.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(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)
36.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0358790
11261727
25001705

prune231.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.8b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite96.0ms

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:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
137.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
165.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07413477
133293295
250013269

prune498.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
5.2b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite295.0ms

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:
15.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
105.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
110.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify256.0ms

Algorithm
egg-herbie
Counts
1160 → 1160
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
0428724836
1500124170

prune2.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
22500×times-frac
11592×add-sqr-sqrt
11591×*-un-lft-identity
8467×add-cube-cbrt
8286×cbrt-prod
1562×distribute-lft-out-- difference-of-squares
903×associate-/l*
784×sqrt-prod
781×distribute-rgt-neg-in
181×div-inv
23×add-exp-log
14×add-cbrt-cube
13×cbrt-undiv div-exp
9×associate-/r*
8×add-log-exp
7×associate-/r/
5×pow1
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 → 6260
Calls
4 calls:
47.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
310.0ms
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
110.0ms
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Algorithm
egg-herbie
Counts
6272 → 6272
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
05544191970

prune25.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.6b

regimes148.0ms

Accuracy

93.9% (1.6b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 31.1b

bsearch155.0ms

Steps
ItersRangePoint
9
3.895668027475672e+69
5.84241073219057e+75
5.94192058439483e+74
6
-8.36501767772797e-260
-8.1135434350231975e-261
-9.977980439923078e-261
9
-1.2294333374423815e+100
-1.4471431684397531e+91
-4.301018409236461e+98

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05341
15341

end0.0ms

sample1.0s

Algorithm
intervals
Results
212.0ms1087×body2560valid
198.0ms5821×body80valid
140.0ms887×body1280valid
94.0ms2899×body80nan
58.0ms456×body640valid
27.0ms99×body5120valid
22.0ms241×body320valid
8.0ms123×body160valid