Details

Time bar (total: 15.3s)

sample86.0ms

Algorithm
intervals
Results
18.0ms31×body2560valid
18.0ms192×body80valid
9.0ms18×body1280valid
8.0ms256×pre80true
3.0ms4×body5120valid
3.0ms7×body640valid
1.0ms2×body320valid
0.0ms2×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
35.0ms
(+ (* (* 4.0 p) p) (* x x))
38.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
50.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (* (* 4.0 p) p) (* x x))
75.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
114.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
103.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.9s

Counts
91 → 91
Iterations

Useful iterations: 3 (675.0ms)

IterNodesCost
01281657
12771506
27731400
320621385
done50001385

prune442.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
8.2b
(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
14.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-exp-log
6×cbrt-prod add-cbrt-cube add-log-exp
5×pow1
4×cbrt-div
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1/3 div-exp
1×cbrt-undiv +-commutative rec-exp pow-flip frac-2neg 1-exp clear-num sum-log div-inv inv-pow
Counts
4 → 68
Calls
4 calls:
7.0ms
(/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
29.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
33.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series738.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
340.0ms
(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
179.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
192.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.3s

Counts
80 → 80
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01641900
13761790
210251580
331171551
done50001536

prune461.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize41.0ms

Local error

Found 4 expressions with local error:

7.7b
(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod add-log-exp
4×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
3×cbrt-prod
2×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×+-commutative pow1/3 sum-log
Counts
4 → 54
Calls
4 calls:
7.0ms
(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
35.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
33.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series703.0ms

Counts
4 → 12
Calls
4 calls:
330.0ms
(+ 1.0 (* (/ 1 (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
93.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
192.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
66 → 66
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01371704
13351370
29841214
329911185
done50001164

prune584.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.6b
(+ 1.0 (/ (/ x (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt
6×sqrt-prod add-log-exp
5×pow1
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+
2×pow1/3
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
4 → 56
Calls
4 calls:
26.0ms
(cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))
49.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))))
43.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series565.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))
109.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))))
84.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
209.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
68 → 68
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01431580
13181478
28391341
323411301
done50001289

prune427.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

regimes226.0ms

Accuracy

85.3% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 14.6b

bsearch91.0ms

Steps
ItersRangePoint
7
-1.9633238247976672e-115
-4.890099577348249e-117
-1.086568352056345e-115

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03471
14571
done4571

end0.0ms

sample2.2s

Algorithm
intervals
Results
635.0ms739×body2560valid
492.0ms6070×body80valid
292.0ms594×body1280valid
254.0ms8000×pre80true
80.0ms311×body640valid
74.0ms58×body5120valid
28.0ms156×body320valid
9.0ms72×body160valid