Details

Time bar (total: 6.4s)

sample41.0ms

Algorithm
intervals
Results
9.0ms203×body80valid
6.0ms31×body1280valid
5.0ms23×body2560valid
3.0ms79×body80nan
3.0ms17×body640valid
1.0ms4×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 32.9b

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))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite145.0ms

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:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
24.0ms
(- (* b b) (* 4.0 (* a c)))
36.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
29.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
07352858
128302769
250012764

prune477.0ms

Filtered
216 candidates to 120 candidates (55.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2088216
Fresh000
Picked101
Done000
Total2098217

Merged error: 6.2b

Counts
217 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite186.0ms

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:
60.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms
(- (* b b) (* 4.0 (* a c)))
35.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
28.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify96.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013658207
150017647

prune804.0ms

Filtered
507 candidates to 205 candidates (40.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5043507
Fresh347
Picked011
Done000
Total5078515

Merged error: 6.2b

Counts
515 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
165×add-sqr-sqrt
67×*-un-lft-identity
58×associate-*r*
49×unswap-sqr
40×add-cube-cbrt times-frac
36×frac-times associate-/r*
34×difference-of-squares
33×associate-*l*
24×sqrt-prod
23×add-exp-log
22×flip3-- flip--
18×associate-*r/
13×*-commutative add-cbrt-cube
12×distribute-lft-out--
10×prod-exp associate-/l* add-log-exp
7×pow1
6×swap-sqr
4×div-exp clear-num cbrt-unprod
3×frac-2neg diff-log un-div-inv
2×cbrt-undiv sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log div-inv
Counts
4 → 213
Calls
4 calls:
58.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
23.0ms
(- (* b b) (* 4.0 (* a c)))
38.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
46.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09272824
150012639

prune537.0ms

Filtered
225 candidates to 140 candidates (62.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2232225
Fresh246
Picked011
Done011
Total2258233

Merged error: 6.2b

Counts
233 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.8b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
17.0b
(- (pow b 2) (pow b 2))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite151.0ms

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:
34.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
9.0ms
(- (pow b 2) (pow b 2))
27.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series178.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
7.0ms
(- (pow b 2) (pow b 2))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012532771
150012450

prune953.0ms

Filtered
270 candidates to 168 candidates (62.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2691270
Fresh055
Picked101
Done022
Total2708278

Merged error: 6.1b

Counts
278 → 8

regimes183.0ms

Accuracy

92.2% (1.9b remaining)

Error of 7.2b against oracle of 5.4b and baseline of 29.5b

bsearch152.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
5.78921681038671e+118
4
2.7062129888597453e-95
4.861630376334293e-95
2.7444235711350233e-95
8
-1.1853128331038075e+151
-1.0790742320216938e+148
-3.6190188158506807e+149

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04524
14524

end0.0ms

sample1.1s

Algorithm
intervals
Results
250.0ms1063×body2560valid
235.0ms5846×body80valid
159.0ms849×body1280valid
104.0ms2863×body80nan
68.0ms463×body640valid
32.0ms105×body5120valid
26.0ms231×body320valid
10.0ms126×body160valid