Details

Time bar (total: 4.5s)

sample46.0ms

Algorithm
intervals
Results
11.0ms206×body80valid
8.0ms26×body2560valid
6.0ms25×body1280valid
4.0ms75×body80nan
2.0ms12×body640valid
1.0ms8×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

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: 32.2b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- 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)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25001735

prune264.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New948102
Fresh000
Picked101
Done000
Total958103

Merged error: 6.0b

Counts
103 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×*-un-lft-identity
14×add-sqr-sqrt
13×add-cbrt-cube
11×add-cube-cbrt
10×fma-def prod-exp add-log-exp
7×pow1 associate-*r*
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 100
Calls
4 calls:
14.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
10.0ms
(+ (- 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)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05141011
12322856
25001843

prune251.0ms

Filtered
112 candidates to 85 candidates (75.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh077
Picked011
Done000
Total1128120

Merged error: 6.0b

Counts
120 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
48×*-un-lft-identity
29×add-sqr-sqrt
28×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×fma-def distribute-lft-out add-log-exp
9×associate-/r/
8×distribute-rgt-neg-in
6×pow1
5×cbrt-undiv flip3-+ flip-+ div-inv
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 134
Calls
4 calls:
12.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(+ (- 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)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05561665
127071442
250011371

prune265.0ms

Filtered
146 candidates to 91 candidates (62.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1451146
Fresh066
Picked011
Done011
Total1459154

Merged error: 6.0b

Counts
154 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (* b b) (* (* 4.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0170540
1665506
22968498
35001488

prune251.0ms

Filtered
78 candidates to 62 candidates (79.5%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New78078
Fresh066
Picked011
Done022
Total78987

Merged error: 6.0b

Counts
87 → 9

regimes186.0ms

Accuracy

88.2% (3.4b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 34.0b

bsearch180.0ms

Steps
ItersRangePoint
7
6.011887282010727e+43
5.675568733030414e+45
7.747263244994283e+43
7
3.8603159558313445e-269
1.7593451497672578e-267
4.0526138277307557e-268
8
-3.9548743960166396e+41
-6.269021281919223e+37
-3.868707050613547e+41

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05029
15229
25229

end0.0ms

sample1.5s

Algorithm
intervals
Results
322.0ms1057×body2560valid
322.0ms5898×body80valid
226.0ms873×body1280valid
146.0ms2907×body80nan
93.0ms447×body640valid
42.0ms108×body5120valid
34.0ms229×body320valid
11.0ms107×body160valid

Profiling

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