Details

Time bar (total: 5.5s)

sample36.0ms

Algorithm
intervals
Results
15.0ms280×body80valid
4.0ms92×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune7.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b
(- (- 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)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (- 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)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04183056
114712008
250011917

prune451.0ms

Filtered
163 candidates to 92 candidates (56.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.1b

localize121.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.5b
(/ (* a c) b)
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-cube-cbrt
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac add-log-exp
7×neg-mul-1
6×associate-/l*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 161
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
19.0ms
(/ (* a c) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06503173
126652081
250022000

prune486.0ms

Filtered
173 candidates to 90 candidates (52.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/r*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 156
Calls
4 calls:
11.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify74.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05453278
121142181
250022098

prune446.0ms

Filtered
168 candidates to 88 candidates (52.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize120.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (+ (- b) (- (* 2.0 (/ a (/ b c))) b)) (* 2.0 a))
4.1b
(/ a (/ b c))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
95×add-sqr-sqrt
90×add-cube-cbrt
80×times-frac
60×prod-diff
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log associate-/r* add-cbrt-cube
10×fma-neg
8×associate-/l* add-log-exp
7×neg-mul-1
6×div-inv
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u distribute-lft-out
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp associate-/r/ cbrt-unprod flip-+
Counts
4 → 210
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ (+ (- b) (- (* 2.0 (/ a (/ b c))) b)) (* 2.0 a))
6.0ms
(/ a (/ b c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(/ (+ (- b) (- (* 2.0 (/ a (/ b c))) b)) (* 2.0 a))
20.0ms
(/ a (/ b c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify101.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08743540
136082402
250022362

prune699.0ms

Filtered
222 candidates to 135 candidates (60.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.8b

regimes283.0ms

Accuracy

87.5% (1.8b remaining)

Error of 8.4b against oracle of 6.6b and baseline of 20.9b

bsearch130.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
6.51740022507215e+112
9
-1.7523220282583258e+27
-2.534584590737501e+21
-1.7289388930153844e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05675
15675

end0.0ms

sample856.0ms

Algorithm
intervals
Results
457.0ms8706×body80valid
142.0ms2892×body80nan