Details

Time bar (total: 5.2s)

sample47.0ms

Algorithm
intervals
Results
10.0ms209×body80valid
7.0ms31×body1280valid
7.0ms25×body2560valid
5.0ms103×body80nan
3.0ms15×body640valid
1.0ms4×body5120valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 28.1b

Counts
2 → 1

localize11.0ms

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))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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:
14.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25001674

prune271.0ms

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: 3.6b

Counts
83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
43.0ms
(- (* 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)))

simplify70.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05251588
125701375
250011308

prune233.0ms

Filtered
126 candidates to 71 candidates (56.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1215126
Fresh437
Picked011
Done000
Total1259134

Merged error: 3.5b

Counts
134 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
333×times-frac
221×*-un-lft-identity
122×add-sqr-sqrt
121×add-cube-cbrt
87×add-exp-log
58×div-exp
50×distribute-lft-out
31×div-inv
25×distribute-rgt-neg-in add-cbrt-cube
21×associate-/r*
17×associate-/r/
15×rec-exp 1-exp
13×cbrt-undiv
12×prod-exp
10×add-log-exp
9×flip3-+ flip-+
7×associate-/l*
5×pow1
3×sqrt-prod
2×flip3-- sqrt-div sum-log flip-- cbrt-unprod
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num associate-/l/
Counts
4 → 263
Calls
4 calls:
18.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011114693
150014134

prune386.0ms

Filtered
275 candidates to 115 candidates (41.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2741275
Fresh167
Picked011
Done011
Total2759284

Merged error: 3.5b

Counts
284 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 1 (* 2.0 a)))
0.5b
(cbrt (/ 1 (* 2.0 a)))
0.5b
(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
17.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
50×cbrt-prod
30×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
18×times-frac
12×pow1 swap-sqr
10×associate-*r* associate-*l*
8×pow1/3 div-inv
6×add-exp-log cbrt-div
4×add-cbrt-cube add-log-exp unswap-sqr
3×sqrt-prod
2×sqrt-div pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square flip3-- sqrt-pow1 pow-plus pow1/2 associate-*r/ associate-*l/ prod-exp *-commutative flip-- cbrt-unprod
Counts
4 → 104
Calls
4 calls:
3.0ms
(cbrt (/ 1 (* 2.0 a)))
3.0ms
(cbrt (/ 1 (* 2.0 a)))
11.0ms
(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(cbrt (/ 1 (* 2.0 a)))
190.0ms
(cbrt (/ 1 (* 2.0 a)))
224.0ms
(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify146.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0275840
11032772
24979678
35003678

prune336.0ms

Filtered
116 candidates to 77 candidates (66.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1160116
Fresh066
Picked011
Done022
Total1169125

Merged error: 3.5b

Counts
125 → 9

regimes216.0ms

Accuracy

89% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 33.9b

bsearch185.0ms

Steps
ItersRangePoint
9
1.7536266209730185e+54
9.156208036690931e+61
3.7405136229447617e+55
9
-4.593581389442884e-257
-3.786974856544585e-264
-3.8324699600337675e-264
4
-2.2709498629311444e+153
-1.3123487377944479e+153
-1.5396067403637575e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05232
15232

end0.0ms

sample1.4s

Algorithm
intervals
Results
296.0ms5872×body80valid
295.0ms1051×body2560valid
207.0ms896×body1280valid
144.0ms2929×body80nan
91.0ms461×body640valid
36.0ms105×body5120valid
30.0ms216×body320valid
10.0ms107×body160valid