Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	142	17
4	275	17
5	458	17
6	672	17
7	802	17
8	985	17
9	1118	17
10	1178	17
11	1179	17
done	1179	17

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.7b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series247.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
65.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
136.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: 3 (294.0ms)

Iter	Nodes	Cost
0	129	985
1	249	962
2	731	854
3	3215	849
done	5001	849

prune443.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
145×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
138×	`sqrt-prod`
22×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`

Counts

4 → 217

Calls

4 calls:

13.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series300.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
54.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
53.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
131.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify971.0ms

Counts

229 → 229

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	318	7057
1	720	6122
2	2302	5559
done	5001	5559

prune519.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
2.7b	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
15.3b	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`log-prod` `times-frac`
15×	`exp-sum`
6×	`pow1` `add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `fma-udef` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

1.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
4.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series288.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
66.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
64.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
137.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify1.6s

Counts

94 → 94

Iterations

Useful iterations: 3 (392.0ms)

Iter	Nodes	Cost
0	180	1536
1	358	1313
2	1017	1155
3	4147	1148
done	5000	1148

prune275.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.1b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
11×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`fma-def` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

17.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
23.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series443.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
69.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
58.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
123.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify692.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	197	1929
1	566	1589
2	2347	1413
done	5000	1413

prune313.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes204.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.5b

bsearch162.0ms

Steps

Iters	Range		Point
9	0.0005333266348582408	74219.82001652327	72489.24391222252
10	-2.739665785741119e+39	-1.2562549030609593e+26	-1.2730222216892933e+26

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	49
1	43	40
done	43	40

end0.0ms

sample482.0ms

Algorithm

intervals

Results

319.0ms

8000×

body

valid