Details

Time bar (total: 4.6s)

sample68.0ms

Algorithm
intervals
Results
11.0ms189×body80valid
11.0ms37×body1280valid
9.0ms27×body2560valid
5.0ms98×body80nan
3.0ms16×body640valid
1.0ms2×body5120valid
1.0ms5×body320valid
0.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite102.0ms

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:
62.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
69.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
38.0ms
(- (* b b) (* (* 3.0 a) c))
61.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0400780
11529686
25002675

prune207.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
2.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.2b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
7.0ms
(- (* b b) (* (* 3.0 a) c))
139.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
98.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 3.0 a) c))
129.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
154.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
62.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06352579
131252333
250012320

prune368.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
1.2b
(- (* b b) (* (* 3.0 a) c))
13.3b
(/ (* 3.0 a) (* 3.0 (* a c)))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
283×add-exp-log
136×div-exp
121×prod-exp
109×add-cbrt-cube
42×cbrt-undiv
41×cbrt-unprod
40×1-exp
32×times-frac
20×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
16×rec-exp
14×associate-/l*
6×add-log-exp
5×pow1 associate-/r/
4×flip3-- flip-- div-inv
3×sqrt-prod
2×frac-times frac-2neg sqrt-div associate-*r/ clear-num associate-/r*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*l/ associate-/l/
Counts
4 → 167
Calls
4 calls:
75.0ms
(/ (/ 1 1) (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
7.0ms
(- (* b b) (* (* 3.0 a) c))
19.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (/ 1 1) (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
38.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
63.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
010752498
150011848

prune279.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ 1 c))
0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
52×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
23×add-exp-log
14×div-exp
13×associate-/r*
10×add-log-exp
9×add-cbrt-cube
7×pow1 rec-exp 1-exp
5×div-inv
4×pow-flip sqrt-prod
3×cbrt-undiv flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- inv-pow difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ remove-double-div
Counts
4 → 130
Calls
4 calls:
10.0ms
(/ 1 (/ 1 c))
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series176.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1 (/ 1 c))
64.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
40.0ms
(- (* b b) (* (* 3.0 a) c))
62.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0505854
12322675
25002573

prune213.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes328.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 28.8b

bsearch158.0ms

Steps
ItersRangePoint
7
3.369701058965069e+122
1.0557394322180785e+124
1.505261368322088e+123
10
-2.8640974595711112e-244
-2.9259838810542055e-263
-2.800575225995961e-254
8
-1.2346399095727716e+156
-1.2603418216603327e+153
-5.6870902931605985e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04426
14426

end0.0ms

sample1.1s

Algorithm
intervals
Results
216.0ms1096×body2560valid
201.0ms5864×body80valid
143.0ms911×body1280valid
95.0ms3004×body80nan
60.0ms464×body640valid
24.0ms101×body5120valid
19.0ms209×body320valid
8.0ms125×body160valid