Details

Time bar (total: 5.8s)

sample59.0ms

Algorithm
intervals
Results
13.0ms189×body80valid
11.0ms35×body2560valid
7.0ms25×body1280valid
4.0ms87×body80nan
3.0ms12×body640valid
1.0ms8×body320valid
1.0ms5×body160valid
0.0ms1×body5120valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b
(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:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms
(- (* b b) (* (* 3.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0433855
11670751
25001736

prune289.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.3b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.4b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite100.0ms

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))))
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)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
151.0ms
(/ (/ (+ 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)))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify146.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
08255119
137383863
250013860

prune546.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.3b
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
11.9b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
54×add-cbrt-cube
48×add-cube-cbrt
40×div-exp
36×sqrt-prod
30×prod-exp
24×distribute-rgt-neg-in
22×cbrt-undiv
21×distribute-lft-neg-in
16×cbrt-unprod
10×fma-neg
8×times-frac 1-exp associate-/l* add-log-exp
7×neg-mul-1
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 185
Calls
4 calls:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
127.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
111.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
09464085
145602694
250012692

prune360.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.9b
(* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
3.3b
(/ (* 1 (/ 3.0 (* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))) (* 3.0 a))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
243×add-exp-log
118×div-exp
101×prod-exp
98×add-sqr-sqrt
89×add-cbrt-cube
82×*-un-lft-identity
64×add-cube-cbrt
60×prod-diff
38×times-frac
37×sqrt-prod
36×cbrt-undiv
31×cbrt-unprod
30×1-exp
25×distribute-rgt-neg-in associate-*r*
21×distribute-lft-neg-in
13×associate-*l*
10×rec-exp fma-neg
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 neg-mul-1
6×unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×div-inv
2×flip3-- sqrt-div diff-log associate-*r/ flip--
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative associate-/l/ associate-/l*
Counts
4 → 249
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
57.0ms
(* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
50.0ms
(/ (* 1 (/ 3.0 (* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))) (* 3.0 a))
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
144.0ms
(* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
169.0ms
(/ (* 1 (/ 3.0 (* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))) (* 3.0 a))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
261 → 261
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013415116
150013597

prune437.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

regimes389.0ms

Accuracy

89.7% (2.8b remaining)

Error of 8.1b against oracle of 5.3b and baseline of 32.3b

bsearch147.0ms

Steps
ItersRangePoint
6
4.706455236749836e+29
5.491842449186372e+30
5.3300268467023164e+29
8
-7.515608282327343e-257
-1.5086419603322717e-259
-1.5314276380606224e-259
7
-2.963931757502914e+119
-3.3757792073266624e+117
-5.955152059551362e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04930
15130
25130

end0.0ms

sample1.1s

Algorithm
intervals
Results
231.0ms1074×body2560valid
214.0ms5758×body80valid
156.0ms915×body1280valid
97.0ms2898×body80nan
60.0ms450×body640valid
31.0ms99×body5120valid
26.0ms227×body320valid
9.0ms132×body160valid