Details

Time bar (total: 10.6s)

sample13.0ms

Algorithm
intervals
Results
6.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
057
176
done76

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize4.0ms

Local error

Found 1 expressions with local error:

13.6b
(/ x (fma x x 1.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
5.0ms
(/ x (fma x x 1.0))

series93.0ms

Counts
1 → 3
Calls
1 calls:
93.0ms
(/ x (fma x x 1.0))

simplify1.4s

Counts
32 → 32
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
068377
1140362
2492332
32678332
done5000332

prune65.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (fma x x 1.0)))
0.0b
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
13.6b
(sqrt (fma x x 1.0))
13.6b
(sqrt (fma x x 1.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 div-exp
8×prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 162
Calls
4 calls:
7.0ms
(/ 1 (sqrt (fma x x 1.0)))
42.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
1.0ms
(sqrt (fma x x 1.0))
2.0ms
(sqrt (fma x x 1.0))

series267.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ 1 (sqrt (fma x x 1.0)))
68.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
52.0ms
(sqrt (fma x x 1.0))
57.0ms
(sqrt (fma x x 1.0))

simplify2.8s

Counts
174 → 174
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02092888
16222599
241562282
done50002280

prune448.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ 1 (fma x x 1.0))
12.9b
(* x (/ 1 (fma x x 1.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log
13×associate-*r*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u rec-exp 1-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 71
Calls
2 calls:
5.0ms
(/ 1 (fma x x 1.0))
23.0ms
(* x (/ 1 (fma x x 1.0)))

series153.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(/ 1 (fma x x 1.0))
83.0ms
(* x (/ 1 (fma x x 1.0)))

simplify1.1s

Counts
77 → 77
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0122880
1297766
21356649
done5001646

prune165.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

12.9b
(* x (* (* (cbrt (/ 1 (fma x x 1.0))) (cbrt (/ 1 (fma x x 1.0)))) (cbrt (/ 1 (fma x x 1.0)))))
13.3b
(cbrt (/ 1 (fma x x 1.0)))
13.3b
(cbrt (/ 1 (fma x x 1.0)))
13.3b
(cbrt (/ 1 (fma x x 1.0)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×cbrt-div
13×pow1 add-exp-log
10×associate-*r/
9×add-cbrt-cube
6×pow-prod-down prod-exp cbrt-unprod
5×frac-times associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* div-inv
1×associate-*r* *-commutative
Counts
4 → 102
Calls
4 calls:
162.0ms
(* x (* (* (cbrt (/ 1 (fma x x 1.0))) (cbrt (/ 1 (fma x x 1.0)))) (cbrt (/ 1 (fma x x 1.0)))))
6.0ms
(cbrt (/ 1 (fma x x 1.0)))
6.0ms
(cbrt (/ 1 (fma x x 1.0)))
6.0ms
(cbrt (/ 1 (fma x x 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* x (* (* (cbrt (/ 1 (fma x x 1.0))) (cbrt (/ 1 (fma x x 1.0)))) (cbrt (/ 1 (fma x x 1.0)))))
303.0ms
(cbrt (/ 1 (fma x x 1.0)))
354.0ms
(cbrt (/ 1 (fma x x 1.0)))
364.0ms
(cbrt (/ 1 (fma x x 1.0)))

simplify1.3s

Counts
114 → 114
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01632144
13741958
216541487
done50011389

prune387.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes56.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch46.0ms

Steps
ItersRangePoint
5
8587103.50349991
32715339.804033544
8839590.603476735
6
-1.1204131191035021e+20
-1.5429656710250222e+19
-9.071674290670007e+19

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02146
12832
done2832

end0.0ms

sample859.0ms

Algorithm
intervals
Results
678.0ms8000×body80valid