Details

Time bar (total: 16.4s)

sample15.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
057
176
done76

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize4.0ms

Local error

Found 1 expressions with local error:

13.2b
(/ x (+ (* x x) 1.0))

rewrite21.0ms

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*
2×associate-/r/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 31
Calls
1 calls:
19.0ms
(/ x (+ (* x x) 1.0))

series90.0ms

Counts
1 → 3
Calls
1 calls:
90.0ms
(/ x (+ (* x x) 1.0))

simplify2.8s

Counts
34 → 34
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
076444
1173384
2462350
31120350
43306350
done5000350

prune90.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (fma x x 1.0)))
0.0b
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
13.1b
(sqrt (fma x x 1.0))
13.1b
(sqrt (fma x x 1.0))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 156
Calls
4 calls:
11.0ms
(/ x (sqrt (fma x x 1.0)))
65.0ms
(* (/ 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))

series480.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(/ x (sqrt (fma x x 1.0)))
116.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
90.0ms
(sqrt (fma x x 1.0))
69.0ms
(sqrt (fma x x 1.0))

simplify3.3s

Counts
168 → 168
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
02142863
15432545
215922085
344512077
done50002077

prune424.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 (sqrt (fma x x 1.0))) (/ 1 (/ (sqrt (fma x x 1.0)) x)))
0.1b
(/ 1 (/ (sqrt (fma x x 1.0)) x))
13.1b
(sqrt (fma x x 1.0))
13.1b
(sqrt (fma x x 1.0))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
354×times-frac
277×add-sqr-sqrt
185×*-un-lft-identity
156×add-cube-cbrt
102×sqrt-prod
98×add-exp-log
71×associate-*r*
49×div-exp
35×unswap-sqr
30×add-cbrt-cube
28×prod-exp
22×associate-*l* associate-/r*
17×rec-exp 1-exp
12×cbrt-undiv
11×pow1
10×div-inv
6×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-flip pow-prod-down associate-/l* inv-pow
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num un-div-inv *-commutative
Counts
4 → 323
Calls
4 calls:
121.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ 1 (/ (sqrt (fma x x 1.0)) x)))
18.0ms
(/ 1 (/ (sqrt (fma x x 1.0)) x))
2.0ms
(sqrt (fma x x 1.0))
2.0ms
(sqrt (fma x x 1.0))

series402.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ 1 (/ (sqrt (fma x x 1.0)) x)))
148.0ms
(/ 1 (/ (sqrt (fma x x 1.0)) x))
71.0ms
(sqrt (fma x x 1.0))
71.0ms
(sqrt (fma x x 1.0))

simplify2.6s

Counts
335 → 335
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03917099
110505754
222244761
done50004611

prune693.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ 1.0 (pow x 5)))
0.3b
(/ 1.0 (pow x 3))
0.5b
(/ 1.0 (pow x 5))
21.0b
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

rewrite717.0ms

Algorithm
rewrite-expression-head
Rules
532×*-un-lft-identity
373×times-frac
240×prod-diff
238×add-sqr-sqrt
225×add-cube-cbrt
129×distribute-lft-out
79×unpow-prod-down
67×cube-prod
52×div-inv
27×sqr-pow
22×cube-mult unpow3
19×associate-/r*
14×add-exp-log
13×fma-def
11×add-log-exp
8×add-cbrt-cube
6×fma-neg div-exp associate-/l*
5×difference-of-squares
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×frac-sub
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ diff-log frac-add pow-exp clear-num sum-log flip-+
1×+-commutative sub-neg flip3-- associate--l+ flip--
Counts
4 → 418
Calls
4 calls:
58.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
17.0ms
(/ 1.0 (pow x 3))
14.0ms
(/ 1.0 (pow x 5))
582.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
41.0ms
(/ 1.0 (pow x 3))
73.0ms
(/ 1.0 (pow x 5))
61.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

simplify2.7s

Counts
430 → 430
Iterations

Useful iterations: done (2.7s)

IterNodesCost
048017448
1106214593
229249875
done50008463

prune655.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes95.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch112.0ms

Steps
ItersRangePoint
10
1.0194597579740466e-06
20796729.49276672
529.597454464039
10
-6045414056204.408
-123.41774798665298
-853997951174.7607

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02145
12831
done2831

end0.0ms

sample515.0ms

Algorithm
intervals
Results
327.0ms8000×body80valid