Details

Time bar (total: 18.0s)

sample77.0ms

Algorithm
intervals
Results
17.0ms69×body80nan
16.0ms42×body2560valid
11.0ms173×body80valid
9.0ms24×body1280valid
4.0ms19×body640valid
2.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify138.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize17.0ms

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))))

rewrite156.0ms

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:
75.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
50.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
106.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01571750
14021650
213221474
349551459
done50001459

prune413.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize17.0ms

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))))

rewrite314.0ms

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:
18.0ms
(- (* b b) (* 4.0 (* a c)))
173.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
106.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series785.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* b b) (* 4.0 (* a c)))
330.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
273.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
150 → 150
Iterations

Useful iterations: 2 (627.0ms)

IterNodesCost
02524460
16173954
225813652
done50003652

prune632.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize19.0ms

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))))

rewrite293.0ms

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:
9.0ms
(- (* b b) (* 4.0 (* a c)))
178.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
88.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* b b) (* 4.0 (* a c)))
285.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
280.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
132.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
148 → 148
Iterations

Useful iterations: 2 (704.0ms)

IterNodesCost
02574174
16763610
228103178
done50013178

prune609.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

localize15.0ms

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) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times 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 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
128.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
117.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(- (* b b) (* 4.0 (* a c)))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
97 → 97
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01832003
14551793
215531565
done50001543

prune350.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.2b

regimes327.0ms

Accuracy

86.5% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 32.7b

bsearch315.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
9
9.448397398655464e-278
1.4829972419072586e-270
9.580019013081131e-278
9
-5.805813140116762e+38
-3.1089471099746935e+33
-7.631292124342714e+35

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03969
14967
done4967

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s1102×body2560valid
764.0ms860×body1280valid
723.0ms5846×body80valid
275.0ms2941×body80nan
160.0ms490×body640valid
116.0ms107×body5120valid
106.0ms227×body320valid
18.0ms105×body160valid