Details

Time bar (total: 5.7s)

sample40.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
7.0ms191×body80valid
4.0ms19×body1280valid
3.0ms82×body80nan
2.0ms16×body640valid
1.0ms7×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

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: 29.8b

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))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
205×add-sqr-sqrt
114×*-un-lft-identity
84×times-frac
58×difference-of-squares
44×unswap-sqr
42×add-cube-cbrt
36×sqrt-prod distribute-lft-out--
32×associate-*l*
24×associate-*r*
14×distribute-rgt-neg-in *-commutative
12×associate-/r*
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×associate-/l*
6×swap-sqr
5×pow1
4×flip3-- flip--
3×diff-log
2×cbrt-undiv associate--l- neg-sub0 sub-neg sqrt-div div-sub div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 204
Calls
4 calls:
42.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
25.0ms
(- (* b b) (* 4.0 (* a c)))
33.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify95.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07282858
127642769
250012764

prune354.0ms

Filtered
216 candidates to 120 candidates (55.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2088216
Fresh000
Picked011
Done000
Total2089217

Merged error: 4.4b

Counts
217 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
606×times-frac
585×add-sqr-sqrt
454×*-un-lft-identity
236×add-cube-cbrt
130×difference-of-squares
108×distribute-lft-out--
97×associate-/r*
96×associate-*l*
87×associate-*r*
72×sqrt-prod
65×unswap-sqr
50×distribute-rgt-neg-in
35×*-commutative
30×associate-/r/
25×add-exp-log
17×associate-/l*
13×add-cbrt-cube
12×div-exp
10×add-log-exp
7×flip3-- flip--
6×pow1 swap-sqr
5×cbrt-undiv div-inv
3×rec-exp diff-log 1-exp prod-exp clear-num remove-double-div
2×sub-neg frac-2neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log cbrt-unprod inv-pow
Counts
4 → 495
Calls
4 calls:
27.0ms
(- (* b b) (* 4.0 (* a c)))
58.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
28.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* 4.0 (* a c)))
116.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify120.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
013588207
150027647

prune615.0ms

Filtered
507 candidates to 203 candidates (40.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New5052507
Fresh437
Picked011
Done011
Total5097516

Merged error: 4.3b

Counts
516 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.5b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
16.6b
(- (pow b 2) (pow b 2))
19.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
174×add-sqr-sqrt
144×*-un-lft-identity
128×times-frac
84×add-cube-cbrt
64×associate-*l*
37×associate-/l*
31×difference-of-squares
30×unswap-sqr
29×associate-/l/
28×associate-*r*
22×unpow-prod-down sqrt-prod
20×distribute-lft-out--
19×add-exp-log
18×frac-times distribute-lft-out
13×add-cbrt-cube
12×associate-/r* unpow2 sqr-pow
11×flip3-+ flip-+
10×distribute-rgt-out-- add-log-exp
9×associate-*l/
7×div-exp *-commutative
5×pow1 div-inv
4×cbrt-undiv frac-2neg prod-exp clear-num
3×swap-sqr
2×flip3-- sqrt-div associate-*r/ sum-log flip-- cbrt-unprod
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp distribute-rgt-neg-in sqrt-pow1 pow1/2 +-inverses diff-log 1-exp neg-log
Counts
4 → 258
Calls
4 calls:
32.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
62.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
11.0ms
(- (pow b 2) (pow b 2))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series182.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms
(- (pow b 2) (pow b 2))
79.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
012452771
150012450

prune591.0ms

Filtered
270 candidates to 168 candidates (62.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2673270
Fresh134
Picked101
Done022
Total2698277

Merged error: 4.3b

Counts
277 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (+ (- 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)))))
19.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
108×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt
30×difference-of-squares
28×distribute-lft-out
26×associate-*l*
22×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×*-commutative associate-/l*
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×distribute-lft-out--
6×swap-sqr
5×pow1 associate-/r*
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 173
Calls
4 calls:
41.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.0ms
(- (* b b) (* 4.0 (* a c)))
32.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
51.0ms
(- (* b b) (* 4.0 (* a c)))
89.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify89.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05832183
123612084
250012071

prune264.0ms

Filtered
185 candidates to 107 candidates (57.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1841185
Fresh235
Picked011
Done022
Total1867193

Merged error: 4.3b

Counts
193 → 7

regimes169.0ms

Accuracy

94.8% (1.2b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 29.0b

bsearch196.0ms

Steps
ItersRangePoint
9
2.8787744468916765e+83
8.390568855339406e+90
2.959250994499172e+90
8
6.240205758057442e-196
3.5796326245549166e-192
8.025898781161617e-196
10
-2.7851241427016145e+159
-9.354797223898085e+144
-8.243400899959915e+147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03822
13822

end0.0ms

sample1.2s

Algorithm
intervals
Results
253.0ms1068×body2560valid
233.0ms5863×body80valid
170.0ms907×body1280valid
123.0ms2983×body80nan
64.0ms415×body640valid
27.0ms236×body320valid
27.0ms93×body5120valid
9.0ms121×body160valid