Details

Time bar (total: 5.2s)

sample292.0ms

Algorithm
intervals
Results
7.0ms37×body2560valid
6.0ms197×body80valid
4.0ms77×body80nan
4.0ms24×body1280valid
2.0ms16×body640valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
0.8b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
10.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0358790
11261727
25001705

prune240.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 162
Calls
4 calls:
14.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
31.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05692100
125611900
250021763

prune284.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
789×times-frac
493×add-sqr-sqrt
406×*-un-lft-identity
320×add-cube-cbrt
86×difference-of-squares
46×sqrt-prod
44×add-exp-log
43×distribute-lft-out--
40×div-inv
32×div-exp
29×associate-/r/
24×associate-/r*
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/l*
8×cbrt-undiv rec-exp 1-exp add-log-exp
5×pow1
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 423
Calls
4 calls:
22.0ms
(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
36.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm
egg-herbie
Counts
435 → 435
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
016867575
150016811

prune624.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

localize11.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
158×add-sqr-sqrt
157×*-un-lft-identity
89×add-cube-cbrt
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
20×sqrt-prod
17×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 206
Calls
4 calls:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07413477
133293295
250013269

prune487.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

regimes274.0ms

Accuracy

90.3% (2.6b remaining)

Error of 8.2b against oracle of 5.7b and baseline of 32.1b

bsearch122.0ms

Steps
ItersRangePoint
6
6254161.133583045
42925490.781275615
25449170.687741734
8
-1.257923433138816e-290
-4.04405824858586e-294
-4.829200214849252e-294
10
-4.4721271386820616e+151
-9.712280864301115e+136
-7.700313305414632e+138

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14424
24424

end0.0ms

sample982.0ms

Algorithm
intervals
Results
201.0ms1045×body2560valid
194.0ms5937×body80valid
135.0ms854×body1280valid
92.0ms2863×body80nan
53.0ms440×body640valid
26.0ms113×body5120valid
20.0ms226×body320valid
7.0ms120×body160valid