Details

Time bar (total: 5.3s)

sample36.0ms

Algorithm
intervals
Results
15.0ms275×body80valid
5.0ms99×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize116.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04062988
114311956
250021869

prune421.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize117.0ms

Local error

Found 4 expressions with local error:

7.3b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
5.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0249759
1969641
24038626
35001624

prune436.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize119.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
22.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 97
Calls
4 calls:
17.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify184.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03621930
19701879
244771859
350011859

prune494.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.9b

localize123.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0139588
1510568
22129564
35001556

prune445.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.9b

regimes185.0ms

Accuracy

92.4% (0.9b remaining)

Error of 8.7b against oracle of 7.7b and baseline of 20.3b

bsearch176.0ms

Steps
ItersRangePoint
9
1.846147638884188e+104
1.7844061428947563e+109
7.447142365186095e+108
8
-5.17073721832495e+150
-9.039588443684179e+147
-4.05734525598461e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05060
15060

end0.0ms

sample887.0ms

Algorithm
intervals
Results
469.0ms8713×body80valid
151.0ms2974×body80nan