Details

Time bar (total: 6.8s)

sample241.0ms

Algorithm
intervals
Results
207.0ms197×body80valid
8.0ms33×body2560valid
5.0ms27×body1280valid
4.0ms116×body80nan
2.0ms13×body640valid
1.0ms7×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
47.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05903305
121012212
250022128

prune337.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
29.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07184221
130992976
250012863

prune350.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
44.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05663514
119662446
250012361

prune334.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) a)
0.2b
(- (* b b) (* 4.0 (* a c)))
6.9b
(- (/ (- b) a) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) a))
21.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
1339×times-frac
946×add-sqr-sqrt
940×*-un-lft-identity
926×add-cube-cbrt
749×prod-diff
323×sqrt-prod
210×distribute-rgt-neg-in
207×distribute-lft-neg-in
69×neg-mul-1
60×div-inv
35×fma-neg
8×add-log-exp
7×distribute-lft-out--
6×add-exp-log add-cbrt-cube associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num frac-sub sub-div
Counts
4 → 889
Calls
4 calls:
7.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (/ (- b) a) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) a)
44.0ms
(- (* b b) (* 4.0 (* a c)))
95.0ms
(- (/ (- b) a) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) a))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify295.0ms

Algorithm
egg-herbie
Counts
901 → 901
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0197644293
1500128209

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.7b

regimes244.0ms

Accuracy

83.4% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 35.0b

bsearch263.0ms

Steps
ItersRangePoint
9
2.6683347110001497e+63
3.895668027475672e+69
1.5763246439716715e+69
9
-6.372026032033847e-139
-5.609109599303715e-148
-6.273278539774699e-139
10
-4.748004806532821e-81
-3.21055753719808e-93
-1.466065355378786e-87
8
-1.832018824537513e-72
-3.025657799658831e-77
-6.771907934379362e-77

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05338
15338

end0.0ms

sample1.1s

Algorithm
intervals
Results
243.0ms1047×body2560valid
221.0ms5813×body80valid
173.0ms932×body1280valid
103.0ms2901×body80nan
69.0ms470×body640valid
30.0ms110×body5120valid
24.0ms220×body320valid
9.0ms120×body160valid