Details

Time bar (total: 5.8s)

sample70.0ms

Algorithm
intervals
Results
17.0ms181×body80valid
16.0ms42×body2560valid
13.0ms41×body1280valid
6.0ms79×body80nan
3.0ms12×body640valid
1.0ms3×body5120valid
1.0ms3×body320valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
21.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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:
11.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0403779
11514685
25002674

prune229.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite92.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06402692
129442439
250012426

prune406.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (- b))
0.1b
(/ (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (- b)) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
21.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite68.0ms

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 div-sub sqrt-prod
2×cbrt-undiv neg-sub0 associate-+r- flip3-- flip3-+ sqrt-div div-exp unsub-neg sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 74
Calls
4 calls:
16.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (- b))
44.0ms
(/ (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (- b)) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (- b))
106.0ms
(/ (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (- b)) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0404795
11601698
25001695

prune206.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 2.0 (* a c))
2.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.8b
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
21.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
191×times-frac
151×add-sqr-sqrt
124×*-un-lft-identity
99×add-exp-log
85×associate-*r*
82×add-cube-cbrt
63×add-cbrt-cube
51×div-exp
29×cbrt-undiv
26×associate-*l* prod-exp
20×distribute-lft-out-- difference-of-squares
16×cbrt-unprod
13×sqrt-prod
10×distribute-rgt-neg-in
9×div-inv
8×add-log-exp unswap-sqr
7×pow1 associate-/r/
5×flip3-- flip--
4×rec-exp 1-exp
3×associate-/l*
2×sqrt-div diff-log
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 217
Calls
4 calls:
3.0ms
(/ 2.0 (* a c))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
105.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ 2.0 (* a c))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
148.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm
egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013313208
150022733

prune537.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

regimes174.0ms

Accuracy

83.9% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 32.5b

bsearch155.0ms

Steps
ItersRangePoint
10
1.6961005291296945e-95
4.32588531784649e-85
1.2529910715609764e-90
10
-5.769371586257069e+162
-1.6124847451767553e+146
-1.4052299045085703e+151

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03315
13315

end0.0ms

sample1.9s

Algorithm
intervals
Results
478.0ms5822×body80valid
424.0ms1083×body2560valid
287.0ms903×body1280valid
218.0ms2984×body80nan
116.0ms452×body640valid
52.0ms113×body5120valid
43.0ms218×body320valid
15.0ms108×body160valid