Details

Time bar (total: 16.1s)

sample79.0ms

Algorithm
intervals
Results
22.0ms81×body80nan
12.0ms37×body2560valid
10.0ms185×body80valid
10.0ms33×body1280valid
4.0ms20×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify179.0ms

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: 35.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
8×add-cube-cbrt add-log-exp
7×times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
4×prod-exp cbrt-unprod
3×flip3-- distribute-rgt-neg-in associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative div-inv
Counts
4 → 83
Calls
4 calls:
26.0ms
(* 4.0 (* a c))
71.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* 4.0 (* a c))
153.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
134.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
121.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
95 → 95
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01741684
14491578
214521410
done50001398

prune371.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.1b
(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.8b
(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite352.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×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 → 141
Calls
4 calls:
70.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
164.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
94.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
234.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
337.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
94.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts
153 → 153
Iterations

Useful iterations: 2 (610.0ms)

IterNodesCost
02534579
16234087
222733753
done50003753

prune577.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
24.4b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
8×add-exp-log add-cbrt-cube
7×times-frac associate-/l* add-log-exp
6×add-cube-cbrt sqrt-prod distribute-lft-out-- difference-of-squares
4×pow1
3×flip3-- distribute-rgt-neg-in flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 65
Calls
3 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
24.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
10.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series368.0ms

Counts
3 → 9
Calls
3 calls:
155.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
118.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
94.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify3.0s

Counts
74 → 74
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01491530
13881437
212521289
346421274
done50011274

prune306.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))))
0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
24.4b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
58×add-sqr-sqrt
57×*-un-lft-identity
30×add-exp-log
29×add-cube-cbrt
20×associate-/r*
18×add-cbrt-cube
14×div-exp distribute-lft-out-- difference-of-squares
11×associate-/r/
10×sqrt-prod
8×add-log-exp
7×cbrt-undiv flip3-- distribute-rgt-neg-in flip--
6×pow1 div-inv
4×prod-exp associate-/l*
3×rec-exp 1-exp
2×frac-2neg sqrt-div diff-log clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log inv-pow
Counts
4 → 144
Calls
4 calls:
59.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))))
103.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
24.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
9.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series666.0ms

Counts
4 → 12
Calls
4 calls:
288.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))))
167.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
100.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
111.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.3s

Counts
156 → 156
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02343968
15553591
216573245
done50003127

prune409.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes244.0ms

Accuracy

85.1% (3.9b remaining)

Error of 9.5b against oracle of 5.6b and baseline of 31.8b

bsearch322.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
6.326287366549383e+74
9
-7.826064039423189e-132
-1.1138670077130767e-140
-5.358830408552925e-132
6
-3.4377365604695865e-95
-7.852755480555329e-96
-8.46693322491602e-96
7
-8.794280737794768e+42
-4.315177351158757e+40
-7.305451620439275e+42

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04078
14876
done4876

end0.0ms

sample3.5s

Algorithm
intervals
Results
777.0ms2933×body80nan
671.0ms5850×body80valid
615.0ms1054×body2560valid
519.0ms924×body1280valid
196.0ms502×body640valid
61.0ms110×body5120valid
47.0ms207×body320valid
16.0ms108×body160valid