Details

Time bar (total: 4.3s)

sample72.0ms

Algorithm
intervals
Results
16.0ms140×body160valid
15.0ms547×pre80true
13.0ms291×body80nan
6.0ms116×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
09116
19116

prune8.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 29.2b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* 4.0 (* a c))))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.2b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
29.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

series66.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
28.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
15.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

simplify49.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049591319
149591319

prune128.0ms

Filtered
62 candidates to 84 candidates (-35.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New78684
Fresh000
Picked101
Done000
Total79685

Merged error: 0.4b

Counts
85 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.2b
(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
0.2b
(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
0.3b
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
51×*-un-lft-identity
29×add-sqr-sqrt add-cube-cbrt
21×associate-/l*
18×add-exp-log add-cbrt-cube
11×distribute-lft-out
8×add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×associate-/r*
4×pow1 flip3-+ flip-+ div-inv
3×div-sub distribute-frac-neg associate-/l/
2×flip3-- frac-2neg sub0-neg prod-exp clear-num flip-- cbrt-unprod
1×+-commutative sub-neg diff-log sum-log
Counts
4 → 119
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
9.0ms
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))

series127.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
60.0ms
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
051033100

prune271.0ms

Filtered
98 candidates to 131 candidates (-33.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New12011131
Fresh415
Picked101
Done000
Total12512137

Merged error: 0.0b

Counts
137 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (pow b 4) (* 4.0 (* (* a c) (+ (* 4.0 (* a c)) (* b b)))))))))
0.3b
(* (* a c) (+ (* 4.0 (* a c)) (* b b)))
0.3b
(/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (pow b 4) (* 4.0 (* (* a c) (+ (* 4.0 (* a c)) (* b b))))))
0.8b
(pow (* 4.0 (* a c)) 3)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×*-un-lft-identity
42×times-frac
30×add-cube-cbrt
24×difference-of-squares
21×sqr-pow
19×add-exp-log add-cbrt-cube
15×pow1
13×associate-/l*
9×unpow-prod-down
7×associate-/r*
6×pow-prod-down prod-exp cbrt-unprod
4×associate-/r/ associate-/l/ distribute-lft-out distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×cbrt-undiv flip3-- frac-2neg div-sub associate-*r/ div-exp clear-num flip-- div-inv
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in sub0-neg unpow3 cube-prod distribute-frac-neg associate-*l* *-commutative
Counts
4 → 144
Calls
4 calls:
23.0ms
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (pow b 4) (* 4.0 (* (* a c) (+ (* 4.0 (* a c)) (* b b)))))))))
9.0ms
(* (* a c) (+ (* 4.0 (* a c)) (* b b)))
15.0ms
(/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (pow b 4) (* 4.0 (* (* a c) (+ (* 4.0 (* a c)) (* b b))))))
5.0ms
(pow (* 4.0 (* a c)) 3)

series152.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (pow b 4) (* 4.0 (* (* a c) (+ (* 4.0 (* a c)) (* b b)))))))))
15.0ms
(* (* a c) (+ (* 4.0 (* a c)) (* b b)))
36.0ms
(/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (pow b 4) (* 4.0 (* (* a c) (+ (* 4.0 (* a c)) (* b b))))))
8.0ms
(pow (* 4.0 (* a c)) 3)

simplify60.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
051425495

prune511.0ms

Filtered
112 candidates to 156 candidates (-39.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1551156
Fresh01111
Picked101
Done000
Total15612168

Merged error: 0b

Counts
168 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
54×times-frac
35×add-sqr-sqrt add-cube-cbrt
21×associate-/l*
19×add-exp-log add-cbrt-cube
12×cbrt-prod
10×distribute-lft-out
7×cbrt-undiv div-exp
6×unpow-prod-down cube-prod associate-/r/
5×pow1 associate-/r*
4×cube-div div-inv add-log-exp
3×pow-unpow flip3-- flip3-+ div-sub distribute-frac-neg flip-- flip-+ associate-/l/
2×cube-mult cbrt-div frac-2neg sub0-neg unpow3 prod-exp clear-num cbrt-unprod sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 143
Calls
4 calls:
16.0ms
(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (cbrt (pow (- (* b b) (* 4.0 (* a c))) 3))))) (* a 2.0))
13.0ms
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (cbrt (pow (- (* b b) (* 4.0 (* a c))) 3)))))
4.0ms
(cbrt (pow (- (* b b) (* 4.0 (* a c))) 3))
5.0ms
(pow (- (* b b) (* 4.0 (* a c))) 3)

series133.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (cbrt (pow (- (* b b) (* 4.0 (* a c))) 3))))) (* a 2.0))
56.0ms
(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (cbrt (pow (- (* b b) (* 4.0 (* a c))) 3)))))
12.0ms
(cbrt (pow (- (* b b) (* 4.0 (* a c))) 3))
20.0ms
(pow (- (* b b) (* 4.0 (* a c))) 3)

simplify46.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
052033504

prune225.0ms

Filtered
99 candidates to 155 candidates (-56.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1541155
Fresh11011
Picked011
Done000
Total15512167

Merged error: 0b

Counts
167 → 12

regimes258.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04026
14026

end0.0ms

sample2.0s

Algorithm
intervals
Results
448.0ms16585×pre80true
408.0ms4477×body160valid
393.0ms8585×body80nan
167.0ms3523×body80valid

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