Details

Time bar (total: 6.2s)

sample70.0ms

Algorithm
intervals
Results
17.0ms188×body80valid
13.0ms31×body1280valid
12.0ms30×body2560valid
7.0ms91×body80nan
4.0ms15×body640valid
2.0ms4×body5120valid
1.0ms5×body320valid
1.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 3.0 a) c))
0.5b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 3.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0433855
11670751
25001736

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms
(/ (/ (+ 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)))))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
145.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
179.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify139.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08255119
137383863
250013860

prune540.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 3.0 a) c))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.6b
(/ (* 3.0 a) (* 3.0 (* a c)))
20.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series200.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 3.0 a) c))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify95.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
05983041
130531925
250021816

prune302.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.4b
(- (* b b) (* (* 3.0 a) c))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
64×add-exp-log *-un-lft-identity
61×prod-diff
60×add-cube-cbrt
40×div-exp
34×sqrt-prod
31×times-frac
25×add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
15×1-exp
14×prod-exp
13×associate-/l*
11×cbrt-undiv fma-neg
10×add-log-exp
7×neg-mul-1
6×rec-exp
5×pow1 flip3-- associate-/r/ flip--
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 195
Calls
4 calls:
19.0ms
(/ (/ 1 1) (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (/ 1 1) (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
47.0ms
(- (* b b) (* (* 3.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify101.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08463812
139322561
250012521

prune318.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

regimes326.0ms

Accuracy

94.9% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 30.0b

bsearch201.0ms

Steps
ItersRangePoint
8
5.408584085660923e+89
6.673576309669011e+92
4.122987415476214e+92
6
-4.407080684076564e-271
-3.922245627457753e-272
-2.511296920996726e-271
7
-1.2511146020293208e+129
-2.5570389401985865e+127
-4.032376794487168e+127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05031
15031

end0.0ms

sample2.1s

Algorithm
intervals
Results
549.0ms5911×body80valid
452.0ms1057×body2560valid
300.0ms846×body1280valid
245.0ms2844×body80nan
131.0ms459×body640valid
49.0ms226×body320valid
46.0ms93×body5120valid
20.0ms128×body160valid