Details

Time bar (total: 16.1s)

sample23.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
057
176
done76

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize10.0ms

Local error

Found 1 expressions with local error:

15.9b
(/ x (fma x x 1.0))

rewrite14.0ms

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:
12.0ms
(/ x (fma x x 1.0))

series118.0ms

Counts
1 → 3
Calls
1 calls:
118.0ms
(/ x (fma x x 1.0))

simplify2.4s

Counts
32 → 32
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
068377
1132362
2327332
3764332
42008332
done5000332

prune108.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

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))))
15.8b
(sqrt (fma x x 1.0))
15.8b
(sqrt (fma x x 1.0))

rewrite94.0ms

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:
15.0ms
(/ 1 (sqrt (fma x x 1.0)))
68.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
2.0ms
(sqrt (fma x x 1.0))
2.0ms
(sqrt (fma x x 1.0))

series333.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1 (sqrt (fma x x 1.0)))
73.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
79.0ms
(sqrt (fma x x 1.0))
74.0ms
(sqrt (fma x x 1.0))

simplify4.2s

Counts
174 → 174
Iterations

Useful iterations: done (4.2s)

IterNodesCost
02092888
15532505
215762049
344122042
done50001913

prune450.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 x) (/ 1.0 (pow x 3)))
0.3b
(/ 1.0 (pow x 5))
0.4b
(/ 1.0 (pow x 3))
19.1b
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

rewrite964.0ms

Algorithm
rewrite-expression-head
Rules
1773×times-frac
1273×add-sqr-sqrt
1222×*-un-lft-identity
1185×add-cube-cbrt
1040×prod-diff
522×associate-+l+
264×unpow-prod-down
252×cube-prod
112×div-inv
92×sqr-pow
82×cube-mult unpow3
30×difference-of-squares
21×fma-def
19×associate-/r*
14×add-exp-log
13×fma-neg
11×add-log-exp
9×distribute-lft-out--
8×add-cbrt-cube
6×div-exp associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out
3×frac-add
2×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num sum-log frac-sub flip--
1×+-commutative associate-+l- flip3-+ flip-+
Counts
4 → 1245
Calls
4 calls:
84.0ms
(- (/ 1 x) (/ 1.0 (pow x 3)))
13.0ms
(/ 1.0 (pow x 5))
9.0ms
(/ 1.0 (pow x 3))
634.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (/ 1 x) (/ 1.0 (pow x 3)))
74.0ms
(/ 1.0 (pow x 5))
47.0ms
(/ 1.0 (pow x 3))
82.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

simplify2.7s

Counts
1257 → 1257
Iterations

Useful iterations: done (2.6s)

IterNodesCost
079751194
1167840828
2355325274
done500124869

prune3.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch54.0ms

Steps
ItersRangePoint
9
3.244205803610274e-06
1902.9075791774285
470.1828671092737
8
-2.6354521979890637e+33
-5.620501265456609e+28
-1.2032692145665368e+31

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02044
12630
done2630

end0.0ms

sample551.0ms

Algorithm
intervals
Results
361.0ms8000×body80valid