Details

Time bar (total: 8.3s)

sample323.0ms

Algorithm
intervals
Results
18.0ms185×body80valid
11.0ms30×body2560valid
8.0ms25×body1280valid
7.0ms99×body80nan
5.0ms20×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
34.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune291.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
3.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.2b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
141.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07613434
134903258
250023250

prune502.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
2.3b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.4b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1827×add-sqr-sqrt
1826×*-un-lft-identity
1346×add-cube-cbrt
267×associate-/l*
240×distribute-lft-out-- difference-of-squares
123×sqrt-prod
120×distribute-rgt-neg-in
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 1152
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
105.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
89.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
109.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify267.0ms

Algorithm
egg-herbie
Counts
1164 → 1164
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
0427024794
1500124128

prune2.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
24×add-sqr-sqrt
16×add-cube-cbrt
13×add-exp-log associate-*r*
11×times-frac
10×fma-def add-log-exp
9×add-cbrt-cube
7×pow1
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ sqrt-prod flip-+ unswap-sqr
2×frac-times flip3-- sqrt-div div-exp associate-*l/ sum-log flip-- cbrt-unprod
1×cbrt-undiv +-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 fma-neg diff-log 1-exp associate-*r/ prod-diff pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 104
Calls
4 calls:
50.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
32.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0479898
12054778
25001731

prune265.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.6b

regimes189.0ms

Accuracy

88.6% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 32.4b

bsearch321.0ms

Steps
ItersRangePoint
7
6.714891876596302e+121
1.686395921989292e+123
2.292661527341346e+122
6
2.4634856426385367e+30
1.375897298344625e+31
4.6383712677255495e+30
11
1.7382738099505427e-22
0.7032085127721847
0.023173574830720484
10
-5.399505147647774e-194
-1.4984247517127078e-204
-1.5120874391809866e-204
8
-2.1136969993533704e+133
-9.628024177185589e+129
-2.1419401754731713e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05637
15837
25837

end0.0ms

sample1.9s

Algorithm
intervals
Results
493.0ms5896×body80valid
409.0ms1085×body2560valid
278.0ms893×body1280valid
219.0ms2929×body80nan
110.0ms442×body640valid
54.0ms117×body5120valid
43.0ms226×body320valid
14.0ms98×body160valid