Details

sample46.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify6.2s

Counts

1 → 1

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	167	17
4	415	17
5	944	17
6	1502	17
7	1837	17
8	2224	17
9	2802	17
10	3764	17
done	5000	17

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize19.0ms

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)
3.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
14.6b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite21.0ms

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)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
7.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series296.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
39.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
80.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
149.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.5s

Counts

71 → 71

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	129	985
1	251	962
2	768	866
3	3365	855
done	5000	851

prune396.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

13.6b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.6b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.6b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.6b	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series625.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
182.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
156.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
151.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.8s

Counts

61 → 61

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	93	1190
1	197	1155
2	615	1008
3	2889	803
done	5001	797

prune421.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

13.6b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.6b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.6b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.6b	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (/ y (cbrt (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

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series1.7s

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
165.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
129.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.2s	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify3.0s

Counts

61 → 61

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	98	1224
1	215	1161
2	678	1015
3	3317	809
done	5000	802

prune376.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.5b	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

14.0ms	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
10.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
29.0ms	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

series522.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
32.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
78.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
193.0ms	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

simplify1.1s

Counts

103 → 103

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	180	1858
1	448	1778
2	1842	1631
done	5000	1629

prune369.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes183.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.1b

bsearch148.0ms

Steps

Iters	Range		Point
7	174.92574374341007	28918.939680702064	28445.437944446025
10	-2676750800.736259	-0.017567295662805446	-662749730.4766326

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	44
1	31	36
done	31	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

753.0ms

8000×

body

valid