Details

Time bar (total: 3.9s)

sample40.0ms

Algorithm
intervals
Results
7.0ms184×body80valid
6.0ms28×body2560valid
6.0ms31×body1280valid
3.0ms91×body80nan
3.0ms20×body640valid
1.0ms5×body5120valid
0.0ms6×body160valid
0.0ms3×body320valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.3b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
61×*-un-lft-identity
60×prod-diff
49×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×pow1 fma-neg
8×add-log-exp
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative div-inv
Counts
4 → 161
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
15.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series253.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* 4.0 (* a c))
91.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06263254
122062163
250012082

prune333.0ms

Filtered
173 candidates to 88 candidates (50.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1649173
Fresh000
Picked101
Done000
Total1659174

Merged error: 5.6b

Counts
174 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
98×*-un-lft-identity
74×times-frac
70×add-cube-cbrt
60×prod-diff
40×sqrt-prod
30×add-exp-log
28×distribute-rgt-neg-in
21×distribute-lft-neg-in
20×associate-/r*
18×add-cbrt-cube
14×div-exp distribute-lft-out-- difference-of-squares
11×associate-/r/
10×fma-neg
8×add-log-exp
7×cbrt-undiv neg-mul-1 flip3-- flip--
6×pow1 div-inv
4×expm1-log1p-u prod-exp log1p-expm1-u associate-/l*
3×rec-exp 1-exp
2×frac-2neg sqrt-div diff-log clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log inv-pow
Counts
4 → 222
Calls
4 calls:
11.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
13.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
106.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07414532
132703232
250023122

prune374.0ms

Filtered
234 candidates to 108 candidates (46.2%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2304234
Fresh538
Picked101
Done000
Total2367243

Merged error: 5.6b

Counts
243 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.3b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×prod-diff
58×*-un-lft-identity
50×add-cube-cbrt
35×sqrt-prod
28×add-exp-log
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×add-cbrt-cube
13×prod-exp
12×pow1
10×fma-neg associate-*l*
8×associate-*r* add-log-exp
7×neg-mul-1 cbrt-unprod
4×expm1-log1p-u flip3-- div-exp pow-prod-down flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac
2×cbrt-undiv frac-times rec-exp sqrt-div diff-log 1-exp associate-*l/ *-commutative
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log un-div-inv div-inv unswap-sqr
Counts
4 → 169
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
15.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
14.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series257.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
92.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06913371
126982189
250022147

prune304.0ms

Filtered
181 candidates to 89 candidates (49.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1801181
Fresh156
Picked011
Done000
Total1817188

Merged error: 5.6b

Counts
188 → 7

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done011
Total077

Merged error: 5.6b

Counts
7 → 7

regimes197.0ms

Accuracy

85% (4.3b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.1b

bsearch69.0ms

Steps
ItersRangePoint
7
6.66182219120084e+105
6.051047097450507e+107
1.0986068905541061e+106
4
-4.559231648305547e-75
-2.6944994336787596e-75
-4.322102267327746e-75

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.2s

Algorithm
intervals
Results
258.0ms1096×body2560valid
237.0ms5817×body80valid
181.0ms941×body1280valid
108.0ms2942×body80nan
66.0ms434×body640valid
36.0ms129×body5120valid
26.0ms236×body320valid
7.0ms92×body160valid