Details

Time bar (total: 4.0s)

sample93.0ms

Algorithm
intervals
Results
13.0ms143×body160valid
9.0ms306×pre80true
8.0ms63×body80valid
7.0ms50×body320valid
3.0ms50×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))
37.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite26.0ms

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))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series63.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(+ (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

prune132.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New76682
Fresh000
Picked101
Done000
Total77683

Merged error: 0.2b

Counts
83 → 6

localize15.0ms

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))
0.2b
(/ (/ (+ 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)))))

rewrite44.0ms

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))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series124.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify114.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06432666
132102408
250012396

prune296.0ms

Filtered
163 candidates to 106 candidates (35.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh325
Picked101
Done000
Total15910169

Merged error: 0b

Counts
169 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.5b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 209
Calls
4 calls:
25.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
18.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
4.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
4.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series130.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
59.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
8.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
19.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify156.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
08544187
144483817
250013736

prune433.0ms

Filtered
221 candidates to 128 candidates (42.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2201221
Fresh279
Picked011
Done000
Total2229231

Merged error: 0b

Counts
231 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(/ (* 4.0 (* a c)) a)
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (* 4.0 (* a c)) a) (neg (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
90×*-un-lft-identity
56×add-sqr-sqrt add-cube-cbrt
32×distribute-lft-neg-in distribute-rgt-neg-in
27×add-exp-log add-cbrt-cube
17×distribute-lft-out
15×associate-/r* div-inv
10×cbrt-undiv div-exp
8×neg-mul-1 associate-/l* add-log-exp
6×prod-exp cbrt-unprod
4×pow1
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ distribute-neg-frac
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- associate-/l/
Counts
4 → 171
Calls
4 calls:
5.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms
(/ (* 4.0 (* a c)) a)
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (/ (* 4.0 (* a c)) a) (neg (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))

series69.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(/ (* 4.0 (* a c)) a)
8.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(/ (/ (* 4.0 (* a c)) a) (neg (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify107.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08172686
143412462
250032436

prune287.0ms

Filtered
183 candidates to 123 candidates (32.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1812183
Fresh257
Picked101
Done011
Total1848192

Merged error: 0b

Counts
192 → 8

regimes194.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02711
12811
22811

end0.0ms

sample1.5s

Algorithm
intervals
Results
449.0ms4771×body160valid
281.0ms9703×pre80true
196.0ms1403×body320valid
90.0ms1826×body80valid
86.0ms1703×body80nan

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