Details

Time bar (total: 7.2s)

sample42.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
8.0ms192×body80valid
5.0ms26×body1280valid
3.0ms83×body80nan
2.0ms12×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune4.0ms

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: 31.0b

Counts
2 → 1

localize17.0ms

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))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×associate-*l* prod-diff
309×*-un-lft-identity
229×add-cube-cbrt
177×associate-*r*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r* distribute-lft-out--
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 541
Calls
4 calls:
48.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
33.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
52.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify228.0ms

Algorithm
egg-herbie
Counts
553 → 553
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
014429181
148926678
250016676

prune570.0ms

Filtered
553 candidates to 170 candidates (30.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New5449553
Fresh000
Picked101
Done000
Total5459554

Merged error: 4.5b

Counts
554 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
756×add-sqr-sqrt
411×prod-diff
369×associate-*l*
364×*-un-lft-identity
264×add-cube-cbrt
198×unswap-sqr
180×associate-*r*
134×sqrt-prod
118×difference-of-squares
87×swap-sqr
78×*-commutative
72×times-frac
50×distribute-lft-out--
42×fma-neg
12×associate-/r*
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 652
Calls
4 calls:
46.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
37.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
49.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
57.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify148.0ms

Algorithm
egg-herbie
Counts
664 → 664
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0164511150
150017916

prune536.0ms

Filtered
664 candidates to 174 candidates (26.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New6622664
Fresh268
Picked011
Done000
Total6649673

Merged error: 4.5b

Counts
673 → 9

localize14.0ms

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))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
665×add-sqr-sqrt
607×*-un-lft-identity
438×times-frac
381×add-cube-cbrt
376×associate-*l*
330×prod-diff
222×associate-*r*
140×unswap-sqr
100×distribute-lft-out
80×*-commutative
75×swap-sqr
71×associate-/r*
53×distribute-rgt-neg-in
30×difference-of-squares
28×associate-/r/
25×add-exp-log
24×sqrt-prod
17×associate-/l*
15×fma-neg
13×add-cbrt-cube
12×div-exp distribute-lft-out--
10×fma-def add-log-exp
6×pow1
5×cbrt-undiv flip3-+ flip-+ div-inv
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in rec-exp 1-exp prod-exp clear-num remove-double-div
2×flip3-- frac-2neg sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log neg-log cbrt-unprod inv-pow
Counts
4 → 761
Calls
4 calls:
63.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
37.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
53.0ms
(- (* b b) (* (* 4.0 a) c))
97.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify180.0ms

Algorithm
egg-herbie
Counts
773 → 773
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0199212865
1500110486

prune839.0ms

Filtered
773 candidates to 244 candidates (31.6%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New7694773
Fresh257
Picked011
Done011
Total77111782

Merged error: 4.5b

Counts
782 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
48×sqrt-prod
44×*-un-lft-identity
36×unswap-sqr
30×difference-of-squares
20×fma-def
18×associate-*l*
12×add-cube-cbrt distribute-lft-out-- add-log-exp
8×distribute-rgt-neg-in
6×pow1 distribute-lft-neg-in swap-sqr *-commutative
4×add-exp-log expm1-log1p-u sqrt-div sum-log add-cbrt-cube log1p-expm1-u distribute-lft-out
2×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 130
Calls
4 calls:
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify157.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
03071124
110471066
242681050
350011046

prune437.0ms

Filtered
142 candidates to 100 candidates (70.4%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1420142
Fresh088
Picked011
Done022
Total14211153

Merged error: 4.5b

Counts
153 → 11

regimes229.0ms

Accuracy

83.3% (4.6b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 33.3b

bsearch151.0ms

Steps
ItersRangePoint
6
5.170278655164064e-52
2.1804079894200568e-51
1.2688336265881624e-51
10
-2.7851241427016145e+159
-9.354797223898085e+144
-6.311729910477647e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03114
13114

end0.0ms

sample1.2s

Algorithm
intervals
Results
262.0ms1031×body2560valid
240.0ms5955×body80valid
165.0ms853×body1280valid
115.0ms2987×body80nan
70.0ms462×body640valid
25.0ms222×body320valid
25.0ms86×body5120valid
8.0ms102×body160valid