Details

Time bar (total: 5.9s)

sample35.0ms

Algorithm
intervals
Results
15.0ms285×body80valid
5.0ms99×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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))
14.0ms
(- (- 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)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04062988
114311956
250021869

prune386.0ms

Filtered
152 candidates to 80 candidates (52.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
4.3b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.3b
(/ (* a c) b)
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 87
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
172.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
18.0ms
(/ (* a c) b)
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0423713
12101628
25002621

prune384.0ms

Filtered
99 candidates to 72 candidates (72.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize136.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.3b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.3b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
30×add-exp-log *-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×associate-/r* add-log-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/ difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 125
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
9.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
201.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07191446
136621263
250011212

prune617.0ms

Filtered
137 candidates to 101 candidates (73.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize126.0ms

Local error

Found 4 expressions with local error:

3.5b
(cbrt (/ c (cbrt b)))
3.5b
(cbrt (/ c (cbrt b)))
4.3b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (* (cbrt (/ c (cbrt b))) (cbrt (/ c (cbrt b))))) (cbrt (/ c (cbrt b))))))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
62×cbrt-prod
42×times-frac
41×*-un-lft-identity
38×add-sqr-sqrt
33×add-cube-cbrt
9×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×sqrt-prod div-inv
2×cbrt-undiv cbrt-div flip3-- distribute-rgt-neg-in pow1/3 sqrt-div div-exp associate-/r/ flip-- difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod associate-/l*
Counts
4 → 114
Calls
4 calls:
4.0ms
(cbrt (/ c (cbrt b)))
4.0ms
(cbrt (/ c (cbrt b)))
14.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (* (cbrt (/ c (cbrt b))) (cbrt (/ c (cbrt b))))) (cbrt (/ c (cbrt b))))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series562.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(cbrt (/ c (cbrt b)))
159.0ms
(cbrt (/ c (cbrt b)))
183.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (* (cbrt (/ c (cbrt b))) (cbrt (/ c (cbrt b))))) (cbrt (/ c (cbrt b))))))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04601627
118001471
250011428

prune724.0ms

Filtered
126 candidates to 106 candidates (84.1%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

regimes315.0ms

Accuracy

93.2% (1.0b remaining)

Error of 7.7b against oracle of 6.8b and baseline of 20.8b

bsearch168.0ms

Steps
ItersRangePoint
7
9.786063674806627e+75
3.1345211132670796e+77
3.0892781849035615e+77
8
-6.693693221964152e+155
-2.9183492048471296e+152
-1.3396975574702294e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06477
16477

end0.0ms

sample838.0ms

Algorithm
intervals
Results
442.0ms8739×body80valid
141.0ms2987×body80nan