Details

Time bar (total: 3.9s)

sample42.0ms

Algorithm
intervals
Results
7.0ms41×body1280valid
7.0ms179×body80valid
5.0ms24×body2560valid
4.0ms111×body80nan
2.0ms17×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.1b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* 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))))

rewrite38.0ms

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-/l*
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-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
15.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* 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))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
42.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify80.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05903305
121012212
250022128

prune477.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15811169
Fresh000
Picked101
Done000
Total15911170

Merged error: 6.4b

Counts
170 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b
(- (* 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))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
19.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms
(- (* 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))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06563422
125942238
250012193

prune271.0ms

Filtered
177 candidates to 90 candidates (50.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1752177
Fresh3710
Picked011
Done000
Total17810188

Merged error: 6.4b

Counts
188 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))
13.3b
(- (- 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))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
57×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
24×add-cube-cbrt *-un-lft-identity
18×pow1/2
15×swap-sqr
10×fma-neg prod-diff
9×flip3-- associate-*r* associate-*l* pow-prod-up flip-- unswap-sqr
8×add-log-exp
6×add-exp-log distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times log1p-expm1-u
2×neg-mul-1 rem-sqrt-square diff-log associate-*r/ associate-*l/
1×associate--l- pow2 neg-sub0 sub-neg pow-plus sqrt-unprod neg-log prod-exp rem-square-sqrt *-commutative cbrt-unprod difference-of-squares
Counts
4 → 156
Calls
4 calls:
14.0ms
(* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))
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))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))
75.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03892093
115961760
250011635

prune327.0ms

Filtered
168 candidates to 97 candidates (57.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1680168
Fresh088
Picked011
Done011
Total16810178

Merged error: 6.4b

Counts
178 → 10

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New000
Fresh077
Picked011
Done022
Total01010

Merged error: 6.4b

Counts
10 → 10

regimes248.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.2b

bsearch121.0ms

Steps
ItersRangePoint
8
2.8028278488416225e+79
7.17624026241226e+82
7.042361471685654e+82
9
-1.3800529096284603e-81
-1.8960304733955153e-90
-2.91890913136631e-83

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.1s

Algorithm
intervals
Results
249.0ms1053×body2560valid
231.0ms5919×body80valid
166.0ms897×body1280valid
111.0ms3046×body80nan
61.0ms427×body640valid
28.0ms95×body5120valid
23.0ms210×body320valid
8.0ms115×body160valid