Details

Time bar (total: 18.3s)

sample93.0ms

Algorithm
intervals
Results
17.0ms191×body80valid
16.0ms29×body2560valid
13.0ms29×body1280valid
8.0ms22×body640valid
7.0ms80×body80nan
3.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify186.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite148.0ms

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:
83.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
26.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (- (- 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)))
105.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.3s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01571750
14021650
213221474
349551459
done50001459

prune341.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
2.4b
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.0b
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite308.0ms

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:
10.0ms
(- (* b b) (* 4.0 (* a c)))
172.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
110.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series737.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* 4.0 (* a c)))
281.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
286.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
102.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
150 → 150
Iterations

Useful iterations: 2 (775.0ms)

IterNodesCost
02524460
16173954
225813652
done50003652

prune606.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* 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)))
8.0b
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite359.0ms

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:
12.0ms
(- (* b b) (* 4.0 (* a c)))
218.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
108.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series863.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (* b b) (* 4.0 (* a c)))
333.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
304.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
137.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts
148 → 148
Iterations

Useful iterations: 2 (719.0ms)

IterNodesCost
02574174
16763610
228103178
done50013178

prune636.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b
(- (* b b) (* 4.0 (* a c)))
11.2b
(/ (* 4.0 (* a c)) (* 2.0 a))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite125.0ms

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:
65.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms
(- (* b b) (* 4.0 (* a c)))
33.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
56.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
114.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
79 → 79
Iterations

Useful iterations: 2 (337.0ms)

IterNodesCost
01461248
13841130
21818966
done5001966

prune292.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

regimes315.0ms

Accuracy

88.2% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 32.0b

bsearch216.0ms

Steps
ItersRangePoint
0
2.0836136179885362e+135
2.1675125417143413e+135
2.1255630798514387e+135
8
-1.5689852653214878e-249
-6.718454253304289e-254
-8.767251655423634e-253
7
-3.4482088762076956e+69
-1.445974953615168e+68
-3.1028950157805323e+69

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03567
14367
done4367

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.4s5783×body80valid
637.0ms1100×body2560valid
472.0ms917×body1280valid
394.0ms2888×body80nan
174.0ms433×body640valid
152.0ms117×body5120valid
91.0ms233×body320valid
16.0ms104×body160valid