Details

Time bar (total: 29.9s)

sample143.0ms

Algorithm
intervals
Results
52.0ms379×body80valid
50.0ms418×body80nan

simplify5.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (239.0ms)

IterNodesCost
02024
14023
29223
326323
457622
5114422
6201022
7422222
done500022

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b
(- (+ 0.91893853320467 (fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))) x)
0.2b
(fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))
6.5b
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
22×add-sqr-sqrt
20×add-cube-cbrt
12×prod-diff
9×times-frac add-log-exp
6×add-exp-log add-cbrt-cube
5×distribute-lft-out
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
3×associate-/r* associate-/l*
2×diff-log fma-udef distribute-lft-out--
1×cbrt-undiv sub-neg flip3-- frac-2neg div-exp associate--l+ clear-num sum-log flip-- div-inv difference-of-squares
Counts
4 → 84
Calls
4 calls:
0.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
45.0ms
(- (+ 0.91893853320467 (fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))) x)
0.0ms
(fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))
6.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series525.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
194.0ms
(- (+ 0.91893853320467 (fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))) x)
174.0ms
(fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))
116.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify2.4s

Counts
96 → 96
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01702468
13662327
29702050
336171854
done50001852

prune609.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b
(- (+ 0.91893853320467 (fma (log x) (- x 0.5) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)))) x)
0.2b
(fma (log x) (- x 0.5) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)))
6.7b
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
29×add-sqr-sqrt
20×add-cube-cbrt
13×add-exp-log associate-*r*
12×prod-diff
11×times-frac
9×add-cbrt-cube add-log-exp
6×pow1
5×distribute-lft-out
4×expm1-log1p-u fma-neg prod-exp log1p-expm1-u
3×associate-*l* unswap-sqr
2×diff-log div-exp cbrt-unprod fma-udef distribute-lft-out--
1×cbrt-undiv sub-neg rec-exp flip3-- 1-exp associate-*r/ pow-prod-down associate--l+ sum-log un-div-inv *-commutative flip-- div-inv difference-of-squares
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
60.0ms
(- (+ 0.91893853320467 (fma (log x) (- x 0.5) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)))) x)
1.0ms
(fma (log x) (- x 0.5) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)))
29.0ms
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

series515.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
185.0ms
(- (+ 0.91893853320467 (fma (log x) (- x 0.5) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)))) x)
157.0ms
(fma (log x) (- x 0.5) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)))
121.0ms
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

simplify3.6s

Counts
105 → 105
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01942728
14482387
212032066
346851846
done50001844

prune529.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (log x) (- x 0.5) (* (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (/ (sqrt 1) (sqrt x))))
0.3b
(/ (sqrt 1) (sqrt x))
3.4b
(* (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (/ (sqrt 1) (sqrt x)))
3.5b
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
153×add-sqr-sqrt
140×times-frac
127×sqrt-prod
91×*-un-lft-identity
85×add-cube-cbrt
40×associate-*r*
22×associate-*l*
21×unswap-sqr
20×add-exp-log add-cbrt-cube
12×associate-/r*
9×associate-/l*
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num
1×frac-times sqrt-undiv associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 219
Calls
4 calls:
1.0ms
(fma (log x) (- x 0.5) (* (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (/ (sqrt 1) (sqrt x))))
16.0ms
(/ (sqrt 1) (sqrt x))
62.0ms
(* (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (/ (sqrt 1) (sqrt x)))
7.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))

series467.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(fma (log x) (- x 0.5) (* (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (/ (sqrt 1) (sqrt x))))
37.0ms
(/ (sqrt 1) (sqrt x))
112.0ms
(* (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (/ (sqrt 1) (sqrt x)))
132.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))

simplify2.4s

Counts
231 → 231
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02845110
17294328
218023824
done50013770

prune840.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt 1) (sqrt x))
1.6b
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x)))
2.1b
(/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x))) (sqrt (sqrt x)))
3.4b
(* (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x))) (sqrt (sqrt x))) (/ (sqrt 1) (sqrt x)))

rewrite468.0ms

Algorithm
rewrite-expression-head
Rules
1432×sqrt-prod
1395×times-frac
1011×add-sqr-sqrt
656×*-un-lft-identity
630×add-cube-cbrt
283×associate-*l*
91×unswap-sqr
40×associate-*r* associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r* div-inv
14×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times sqrt-undiv associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 892
Calls
4 calls:
8.0ms
(/ (sqrt 1) (sqrt x))
8.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x)))
28.0ms
(/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x))) (sqrt (sqrt x)))
326.0ms
(* (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x))) (sqrt (sqrt x))) (/ (sqrt 1) (sqrt x)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (sqrt 1) (sqrt x))
120.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x)))
93.0ms
(/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x))) (sqrt (sqrt x)))
131.0ms
(* (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (sqrt x))) (sqrt (sqrt x))) (/ (sqrt 1) (sqrt x)))

simplify3.3s

Counts
904 → 904
Iterations

Useful iterations: done (3.2s)

IterNodesCost
068329747
1190226637
2485123198
done500023193

prune3.5s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.2b

regimes368.0ms

Accuracy

79.5% (0.4b remaining)

Error of 4.4b against oracle of 3.9b and baseline of 6.1b

bsearch71.0ms

Steps
ItersRangePoint
5
1.4596706504407988e+49
4.5083813150567236e+49
3.096956618497268e+49

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03353
14153
done4153

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.5s11398×body80nan
1.3s11564×body80valid