Details

Time bar (total: 6.6s)

sample97.0ms

Algorithm
intervals
Results
22.0ms120×body320valid
19.0ms528×pre80true
17.0ms272×body80nan
11.0ms88×body160valid
4.0ms16×body640valid
2.0ms32×body80valid

simplify11.0ms

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: 50.9b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
23.9b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite28.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series342.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0396773
11550683
25001673

prune180.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New80282
Fresh000
Picked101
Done000
Total81283

Merged error: 0.1b

Counts
83 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series655.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
231.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
296.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06432666
132102408
250012396

prune411.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1567163
Fresh011
Picked101
Done000
Total1578165

Merged error: 0b

Counts
165 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
0.5b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
36.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
11.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
11.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))

series752.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
339.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
36.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
95.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09925286
150014711

prune664.0ms

Filtered
247 candidates to 145 candidates (58.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2470247
Fresh077
Picked011
Done000
Total2478255

Merged error: 0b

Counts
255 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
0.2b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
92×add-cbrt-cube
73×prod-exp
46×div-exp
41×cbrt-unprod
26×cbrt-undiv
14×add-sqr-sqrt
12×*-un-lft-identity
9×pow1
8×add-cube-cbrt rec-exp 1-exp
7×associate-*r*
6×add-log-exp
5×flip3-- times-frac associate-*l* associate-/r/ flip--
4×frac-times associate-*r/ associate-/l*
3×sub-neg div-inv
2×distribute-rgt-in pow-flip frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×distribute-rgt-neg-in diff-log sqrt-prod *-commutative inv-pow unswap-sqr
Counts
4 → 139
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
18.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series430.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
240.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
128.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08162127
150011586

prune244.0ms

Filtered
151 candidates to 72 candidates (47.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1510151
Fresh066
Picked011
Done011
Total1518159

Merged error: 0b

Counts
159 → 8

regimes112.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03121
13421
23421

end0.0ms

sample2.1s

Algorithm
intervals
Results
495.0ms3605×body320valid
457.0ms16502×pre80true
404.0ms8502×body80nan
280.0ms2973×body160valid
95.0ms516×body640valid
44.0ms906×body80valid

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