Details

Time bar (total: 18.1s)

sample88.0ms

Algorithm
intervals
Results
20.0ms42×body2560valid
19.0ms173×body80valid
9.0ms24×body1280valid
6.0ms19×body640valid
5.0ms69×body80nan
2.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify194.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite632.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
552.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
107.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(- (* b b) (* 4.0 (* a c)))
121.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01571750
14021650
213221474
349551459
done50001459

prune320.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize38.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
2.4b
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.8b
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
14.0ms
(- (* b b) (* 4.0 (* a c)))
174.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
85.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series728.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* 4.0 (* a c)))
298.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
276.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
83.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
150 → 150
Iterations

Useful iterations: 2 (602.0ms)

IterNodesCost
02524460
16173954
225813652
done50003652

prune666.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize45.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
2.5b
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.8b
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite419.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
51×add-exp-log
42×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp
14×difference-of-squares
10×sqrt-prod
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r* distribute-lft-out--
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 136
Calls
4 calls:
10.0ms
(- (* b b) (* 4.0 (* a c)))
248.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
136.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (* b b) (* 4.0 (* a c)))
339.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
264.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
148 → 148
Iterations

Useful iterations: 2 (830.0ms)

IterNodesCost
02574174
16763610
228103178
done50013178

prune615.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b
(- (* b b) (* 4.0 (* a c)))
15.2b
(/ (* 4.0 (* a c)) (* 2.0 a))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
63.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
57.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
107.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
79 → 79
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
01461248
13841130
21818966
done5001966

prune266.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.2b

regimes413.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.7b

bsearch302.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
11
-2.859335985249397e-307
9.448397398655464e-278
2.6770716389234043e-300
9
-1.4642911230069481e+159
-8.435593739772907e+149
-3.5132588248780117e+152

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03359
13959
done3959

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s1102×body2560valid
852.0ms5846×body80valid
423.0ms860×body1280valid
273.0ms2941×body80nan
171.0ms490×body640valid
65.0ms107×body5120valid
49.0ms227×body320valid
14.0ms105×body160valid