Details

Time bar (total: 16.4s)

sample13.0ms

Algorithm
intervals
Results
6.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
057
176
done76

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize9.0ms

Local error

Found 1 expressions with local error:

13.2b
(/ x (fma x x 1.0))

rewrite13.0ms

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:
11.0ms
(/ x (fma x x 1.0))

series111.0ms

Counts
1 → 3
Calls
1 calls:
111.0ms
(/ x (fma x x 1.0))

simplify2.6s

Counts
32 → 32
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
068377
1132362
2327332
3764332
42008332
done5000332

prune97.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

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))

rewrite110.0ms

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:
12.0ms
(/ x (sqrt (fma x x 1.0)))
80.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
2.0ms
(sqrt (fma x x 1.0))
3.0ms
(sqrt (fma x x 1.0))

series454.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ x (sqrt (fma x x 1.0)))
110.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
67.0ms
(sqrt (fma x x 1.0))
69.0ms
(sqrt (fma x x 1.0))

simplify3.5s

Counts
168 → 168
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
02142863
15432545
215922085
344512077
done50002077

prune506.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (/ (/ 1 (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0)))) (/ x (sqrt (sqrt (fma x x 1.0)))))
13.1b
(sqrt (fma x x 1.0))
13.1b
(sqrt (fma x x 1.0))
13.1b
(sqrt (fma x x 1.0))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
543×times-frac
473×add-sqr-sqrt
447×sqrt-prod
234×*-un-lft-identity
210×add-cube-cbrt
202×associate-*l*
64×unswap-sqr
39×add-exp-log
31×associate-*r*
25×add-cbrt-cube
17×div-exp
11×div-inv
10×prod-exp
9×pow1 cbrt-undiv
6×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×rec-exp 1-exp
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 372
Calls
4 calls:
202.0ms
(* (/ (/ 1 (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0)))) (/ x (sqrt (sqrt (fma x x 1.0)))))
3.0ms
(sqrt (fma x x 1.0))
3.0ms
(sqrt (fma x x 1.0))
4.0ms
(sqrt (fma x x 1.0))

series256.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (/ (/ 1 (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0)))) (/ x (sqrt (sqrt (fma x x 1.0)))))
58.0ms
(sqrt (fma x x 1.0))
63.0ms
(sqrt (fma x x 1.0))
59.0ms
(sqrt (fma x x 1.0))

simplify2.0s

Counts
384 → 384
Iterations

Useful iterations: done (2.0s)

IterNodesCost
034410872
1103710319
225928463
done50007860

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize14.0ms

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)))

rewrite805.0ms

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:
49.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
15.0ms
(/ 1.0 (pow x 3))
8.0ms
(/ 1.0 (pow x 5))
670.0ms
(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (/ 1 x) (/ 1.0 (pow x 5)))
78.0ms
(/ 1.0 (pow x 3))
91.0ms
(/ 1.0 (pow x 5))
62.0ms
(- (+ (/ 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

prune638.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch91.0ms

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

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02044
12630
done2630

end0.0ms

sample546.0ms

Algorithm
intervals
Results
345.0ms8000×body80valid