Details

Time bar (total: 5.5s)

sample43.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms180×body80valid
6.0ms35×body1280valid
4.0ms110×body80nan
2.0ms14×body640valid
1.0ms4×body5120valid
0.0ms4×body320valid
0.0ms5×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.7b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
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 cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
45.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
50.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify89.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06212253
124432157
250032140

prune322.0ms

Filtered
190 candidates to 109 candidates (42.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1828190
Fresh000
Picked011
Done000
Total1829191

Merged error: 5.0b

Counts
191 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
438×times-frac
414×*-un-lft-identity
321×add-sqr-sqrt
188×add-cube-cbrt
100×distribute-lft-out
82×associate-*l*
71×associate-/r*
63×associate-*r*
57×unswap-sqr
50×distribute-rgt-neg-in
30×difference-of-squares
28×associate-/r/
27×*-commutative
25×add-exp-log
24×sqrt-prod
17×associate-/l*
13×add-cbrt-cube
12×div-exp distribute-lft-out--
10×add-log-exp
6×pow1 swap-sqr
5×cbrt-undiv flip3-+ flip-+ div-inv
3×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- sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log neg-log cbrt-unprod inv-pow
Counts
4 → 398
Calls
4 calls:
57.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
52.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
410 → 410
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
011755935
150015465

prune496.0ms

Filtered
410 candidates to 170 candidates (58.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4073410
Fresh257
Picked101
Done011
Total4109419

Merged error: 5.0b

Counts
419 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
48×sqrt-prod
38×*-un-lft-identity
36×unswap-sqr
30×difference-of-squares
18×associate-*l*
12×distribute-lft-out-- add-log-exp
6×pow1 add-cube-cbrt swap-sqr *-commutative
4×add-exp-log sqrt-div sum-log add-cbrt-cube distribute-lft-out
2×+-commutative neg-sub0 associate-+l- rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 102
Calls
4 calls:
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
02841054
19451012
23750996
35001980

prune518.0ms

Filtered
114 candidates to 72 candidates (36.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh077
Picked011
Done011
Total1149123

Merged error: 5.0b

Counts
123 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.1b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
18.8b
(- (pow b 2) (pow b 2))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
200×*-un-lft-identity
132×add-sqr-sqrt
84×times-frac
59×associate-*l*
52×distribute-lft-out
50×add-cube-cbrt
42×distribute-lft-out--
33×difference-of-squares
26×unswap-sqr
25×sqrt-prod
24×associate-*r*
22×unpow-prod-down
12×associate-/r* unpow2 sqr-pow
11×*-commutative
10×distribute-rgt-out-- add-log-exp
9×add-exp-log add-cbrt-cube
7×associate-/l*
5×pow1
3×flip3-- diff-log swap-sqr flip--
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 +-inverses div-sub neg-log prod-exp clear-num cbrt-unprod flip-+ div-inv
Counts
4 → 221
Calls
4 calls:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
8.0ms
(- (pow b 2) (pow b 2))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms
(- (pow b 2) (pow b 2))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify214.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 2 (190.0ms)

IterNodesCost
07292218
140391793
250011786

prune363.0ms

Filtered
233 candidates to 118 candidates (49.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2312233
Fresh246
Picked101
Done112
Total2357242

Merged error: 5.0b

Counts
242 → 7

regimes186.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.9b

bsearch105.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
8
-2.0030864347859544e-273
-1.6635287532714566e-276
-2.826980895315778e-274
8
-8.122802074996069e+81
-2.6359676868927157e+78
-8.403193116555128e+80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14024

end0.0ms

sample1.1s

Algorithm
intervals
Results
238.0ms1098×body2560valid
217.0ms5797×body80valid
161.0ms885×body1280valid
99.0ms2780×body80nan
66.0ms464×body640valid
31.0ms116×body5120valid
26.0ms249×body320valid
8.0ms117×body160valid