Details

Time bar (total: 4.5s)

sample49.0ms

Algorithm
intervals
Results
10.0ms194×body80valid
9.0ms33×body2560valid
5.0ms23×body1280valid
5.0ms96×body80nan
3.0ms18×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

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: 34.9b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
25.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0403779
11514685
25002674

prune216.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74882
Fresh000
Picked101
Done000
Total75883

Merged error: 6.8b

Counts
83 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
2.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
144.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06282579
129542333
250012320

prune360.0ms

Filtered
160 candidates to 106 candidates (66.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1564160
Fresh347
Picked101
Done000
Total1608168

Merged error: 6.7b

Counts
168 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
13.0b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
9.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series203.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0413627
12231543
25001535

prune183.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New81182
Fresh167
Picked101
Done000
Total83790

Merged error: 6.7b

Counts
90 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
25.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
13×add-cube-cbrt associate-*l*
10×times-frac add-log-exp
9×add-exp-log add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg distribute-lft-out-- difference-of-squares
3×diff-log
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
15.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0442997
11811906
25001896

prune216.0ms

Filtered
101 candidates to 73 candidates (72.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New992101
Fresh066
Picked011
Done000
Total999108

Merged error: 6.7b

Counts
108 → 9

regimes174.0ms

Accuracy

92% (1.9b remaining)

Error of 7.4b against oracle of 5.4b and baseline of 29.3b

bsearch173.0ms

Steps
ItersRangePoint
7
0.008549975533169097
1.4731263457460937
1.4443031837246074
8
-1.7832961101597004e-170
-3.712432627983841e-174
-3.760762857445126e-174
9
-8.023912243850115e+115
-1.183450711292762e+109
-1.173641368412307e+114

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04726
14726

end0.0ms

sample1.4s

Algorithm
intervals
Results
327.0ms1092×body2560valid
313.0ms5847×body80valid
221.0ms875×body1280valid
147.0ms2883×body80nan
85.0ms451×body640valid
40.0ms111×body5120valid
33.0ms233×body320valid
11.0ms118×body160valid