Details

Time bar (total: 15.9s)

sample26.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
057
176
done76

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize9.0ms

Local error

Found 1 expressions with local error:

13.4b
(/ x (+ (* x x) 1.0))

rewrite29.0ms

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:
27.0ms
(/ x (+ (* x x) 1.0))

series99.0ms

Counts
1 → 3
Calls
1 calls:
99.0ms
(/ x (+ (* x x) 1.0))

simplify2.7s

Counts
34 → 34
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
076444
1173384
2462350
31120350
43306350
done5000350

prune103.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
0.0b
(/ 1 (sqrt (fma x x 1.0)))
13.3b
(sqrt (fma x x 1.0))
13.3b
(sqrt (fma x x 1.0))

rewrite84.0ms

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:
57.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
14.0ms
(/ 1 (sqrt (fma x x 1.0)))
3.0ms
(sqrt (fma x x 1.0))
3.0ms
(sqrt (fma x x 1.0))

series385.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
121.0ms
(/ 1 (sqrt (fma x x 1.0)))
97.0ms
(sqrt (fma x x 1.0))
86.0ms
(sqrt (fma x x 1.0))

simplify3.8s

Counts
174 → 174
Iterations

Useful iterations: done (3.8s)

IterNodesCost
02092888
15532505
215772049
343932042
done50011913

prune795.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

5.4b
(/ x (- (pow x 4) (* 1.0 1.0)))
19.4b
(* (/ x (- (pow x 4) (* 1.0 1.0))) (- (* x x) 1.0))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
37×times-frac
26×add-cube-cbrt *-un-lft-identity
24×associate-*l*
22×difference-of-squares
9×add-exp-log add-cbrt-cube
7×unpow-prod-down sqr-pow
6×prod-diff associate-/r*
5×distribute-rgt-in distribute-lft-in
4×pow1 flip3-- associate-*r* associate-/r/ flip--
3×associate-/l*
2×cbrt-undiv expm1-log1p-u frac-times sub-neg associate-*r/ div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
2 → 103
Calls
2 calls:
38.0ms
(/ x (- (pow x 4) (* 1.0 1.0)))
147.0ms
(* (/ x (- (pow x 4) (* 1.0 1.0))) (- (* x x) 1.0))

series332.0ms

Counts
2 → 6
Calls
2 calls:
181.0ms
(/ x (- (pow x 4) (* 1.0 1.0)))
150.0ms
(* (/ x (- (pow x 4) (* 1.0 1.0))) (- (* x x) 1.0))

simplify2.0s

Counts
109 → 109
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02312101
15661956
217191793
done50001507

prune428.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ 1.0 (pow x 5)))
0.0b
(/ 1.0 (pow x 5))
0.4b
(/ 1.0 (pow x 3))
18.5b
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

rewrite615.0ms

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:
37.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
7.0ms
(/ 1.0 (pow x 5))
10.0ms
(/ 1.0 (pow x 3))
522.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
84.0ms
(/ 1.0 (pow x 5))
59.0ms
(/ 1.0 (pow x 3))
51.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

simplify2.6s

Counts
430 → 430
Iterations

Useful iterations: done (2.6s)

IterNodesCost
048017448
1106214593
229279875
done50008463

prune662.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch111.0ms

Steps
ItersRangePoint
10
8.937283511995443e-05
28405617999702.24
434.3260566585274
8
-3122934099202797.0
-115102859795.89769
-4377789621347.088

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02653
13339
done3339

end0.0ms

sample479.0ms

Algorithm
intervals
Results
338.0ms8000×body80valid