Details

Time bar (total: 5.3s)

sample37.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
7.0ms189×body80valid
4.0ms25×body1280valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms8×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize14.0ms

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)))

rewrite56.0ms

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:
35.0ms
(/ (+ (- 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)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms
(- (* b b) (* (* 3.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms
(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

prune231.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

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)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×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 → 154
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
27.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
147.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
176.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06472692
131142439
250012426

prune450.0ms

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)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
54×add-cbrt-cube
40×div-exp
30×prod-exp
22×cbrt-undiv
20×add-sqr-sqrt
19×*-un-lft-identity
16×cbrt-unprod
8×times-frac 1-exp associate-/l* add-log-exp
7×add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
3×flip3-- distribute-rgt-neg-in 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 → 107
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
38.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
126.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
104.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify99.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07701662
139921314
250031302

prune264.0ms

Pruning

12 alts after pruning (12 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)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
243×add-exp-log
118×div-exp
101×prod-exp
89×add-cbrt-cube
57×add-sqr-sqrt
41×*-un-lft-identity
38×times-frac
36×cbrt-undiv
31×cbrt-unprod
30×1-exp
25×associate-*r*
23×add-cube-cbrt
13×associate-*l*
10×rec-exp
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×unswap-sqr
4×distribute-rgt-neg-in
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 → 171
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
59.0ms
(* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
51.0ms
(/ (* 1 (/ 3.0 (* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))) (* 3.0 a))
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
153.0ms
(* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
155.0ms
(/ (* 1 (/ 3.0 (* (/ 1 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))) (* 3.0 a))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011672689
150012125

prune344.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes396.0ms

Accuracy

89.7% (2.8b remaining)

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

bsearch137.0ms

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
244.0ms1074×body2560valid
216.0ms5758×body80valid
169.0ms915×body1280valid
112.0ms2898×body80nan
64.0ms450×body640valid
27.0ms99×body5120valid
27.0ms227×body320valid
9.0ms132×body160valid