Details

Time bar (total: 3.8s)

sample34.0ms

Algorithm
intervals
Results
7.0ms36×body2560valid
6.0ms194×body80valid
4.0ms25×body1280valid
3.0ms100×body80nan
2.0ms13×body640valid
1.0ms4×body5120valid
1.0ms7×body320valid
0.0ms1×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b
(- (* b_2 b_2) (* a c))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
35.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(- (* b_2 b_2) (* a c))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0368965
11241910
25001901

prune242.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b
(- (* b_2 b_2) (* a c))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 177
Calls
4 calls:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
99.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05912458
127062226
250012071

prune278.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b
(- (* b_2 b_2) (* a c))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
32.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms
(- (- 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)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0368965
11241910
25001901

prune231.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
33.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0428881
11823791
25001771

prune210.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes248.0ms

Accuracy

88.2% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 31.9b

bsearch130.0ms

Steps
ItersRangePoint
7
6.714891876596302e+121
1.686395921989292e+123
2.8930707274762056e+122
7
-2.0528466669849744e-181
-2.126384722856045e-183
-6.579412753399757e-183
9
-3.648537902993238e+76
-1.3447839841174185e+67
-1.8746290509448952e+74

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04426
14826
24826

end0.0ms

sample969.0ms

Algorithm
intervals
Results
205.0ms1094×body2560valid
193.0ms5865×body80valid
133.0ms873×body1280valid
87.0ms2925×body80nan
56.0ms452×body640valid
23.0ms102×body5120valid
23.0ms239×body320valid
7.0ms116×body160valid