Details

Time bar (total: 5.2s)

sample37.0ms

Algorithm
intervals
Results
7.0ms209×body80valid
7.0ms34×body2560valid
4.0ms22×body1280valid
3.0ms79×body80nan
2.0ms18×body640valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite58.0ms

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:
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms
(- (* b b) (* (* 3.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0400780
11529686
25002675

prune226.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
4.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.6b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite84.0ms

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:
3.0ms
(- (* b b) (* (* 3.0 a) c))
44.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
26.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 3.0 a) c))
152.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
183.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06352579
131252333
250012320

prune411.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* b b) (- 0 (* 3.0 (* a c))))
4.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
10.6b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))))
23.5b
(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

rewrite144.0ms

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
9×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1
4×div-inv
3×flip3-- flip3-+ flip-- flip-+ associate-/l/
2×associate-+r+ frac-2neg sub0-neg sqrt-div prod-exp clear-num sum-log cbrt-unprod
1×+-commutative associate-+r- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log unsub-neg
Counts
4 → 153
Calls
4 calls:
6.0ms
(+ (* b b) (- 0 (* 3.0 (* a c))))
72.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
50.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))))
10.0ms
(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* b b) (- 0 (* 3.0 (* a c))))
150.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
184.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))))
74.0ms
(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

simplify106.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06442793
131212522
250022507

prune414.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))
1.2b
(+ (* b b) (- 0 (* 3.0 (* a c))))
14.2b
(/ (* 3.0 a) (* 3.0 (* a c)))
23.5b
(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
13×add-log-exp
10×add-sqr-sqrt
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×diff-log
2×sub-neg associate-+r+ flip3-+ sub0-neg sqrt-div sum-log flip-+ distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- neg-sub0 associate-+r- rem-sqrt-square flip3-- distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 unsub-neg neg-log clear-num associate-/r* flip-- div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
21.0ms
(- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))
6.0ms
(+ (* b b) (- 0 (* 3.0 (* a c))))
8.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
191.0ms
(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

series203.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (+ (* b b) (- 0 (* 3.0 (* a c))))))
44.0ms
(+ (* b b) (- 0 (* 3.0 (* a c))))
11.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
72.0ms
(sqrt (+ (* b b) (- 0 (* 3.0 (* a c)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0429699
12441575
25003545

prune191.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

regimes320.0ms

Accuracy

94.1% (1.4b remaining)

Error of 6.7b against oracle of 5.3b and baseline of 29.5b

bsearch191.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
1.8676563684114658e+102
11
-6.180552121099898e-304
6.534853956177064e-292
1.0719826190049434e-308
10
-3.0823188855845346e+100
-4.9258557020066e+89
-7.478383220944118e+90

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05629
16629
27229
37329
47529
57529

end0.0ms

sample1.1s

Algorithm
intervals
Results
225.0ms1070×body2560valid
211.0ms5838×body80valid
160.0ms884×body1280valid
99.0ms2849×body80nan
66.0ms497×body640valid
29.0ms102×body5120valid
22.0ms219×body320valid
7.0ms104×body160valid