Details

sample70.0ms

Algorithm

intervals

Results

30.0ms

542×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (156.0ms)

Iter	Nodes	Cost
0	11	13
1	21	13
2	52	13
3	171	13
4	496	12
5	1885	12
done	5001	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(- t (* z z))
5.0b	(fma (* y 4.0) (- t (* z z)) (* x x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `difference-of-squares`

Counts

2 → 31

Calls

2 calls:

18.0ms	(- t (* z z))
1.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))

series220.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- t (* z z))
164.0ms	(fma (* y 4.0) (- t (* z z)) (* x x))

simplify601.0ms

Counts

37 → 37

Iterations

Useful iterations: done (599.0ms)

Iter	Nodes	Cost
0	65	421
1	155	415
2	639	357
done	5000	349

prune227.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.3b

localize44.0ms

Local error

Found 3 expressions with local error:

0.6b	(cbrt t)
0.7b	(pow (cbrt t) 3)
5.0b	(fma (* y 4.0) (+ (fma z (- z) (pow (cbrt t) 3)) (* z (+ (- z) z))) (* x x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `pow1/3`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

3 → 55

Calls

3 calls:

1.0ms	(cbrt t)
5.0ms	(pow (cbrt t) 3)
1.0ms	(fma (* y 4.0) (+ (fma z (- z) (pow (cbrt t) 3)) (* z (+ (- z) z))) (* x x))

series829.0ms

Counts

3 → 9

Calls

3 calls:

277.0ms	(cbrt t)
328.0ms	(pow (cbrt t) 3)
224.0ms	(fma (* y 4.0) (+ (fma z (- z) (pow (cbrt t) 3)) (* z (+ (- z) z))) (* x x))

simplify1.8s

Counts

64 → 64

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	84	631
1	229	475
2	790	391
3	3315	362
done	5000	351

prune369.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 4.0 (* t y) (* x x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 4.0 (* t y) (* x x))

series87.0ms

Counts

1 → 3

Calls

1 calls:

87.0ms

(fma 4.0 (* t y) (* x x))

simplify1.9s

Counts

13 → 13

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	20	140
1	30	137
2	79	121
3	272	121
4	1295	121
done	5000	121

prune109.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 4.0 (* t y) (* x x))) (cbrt (fma 4.0 (* t y) (* x x))))
3.3b	(cbrt (fma 4.0 (* t y) (* x x)))
3.3b	(cbrt (fma 4.0 (* t y) (* x x)))
3.3b	(cbrt (fma 4.0 (* t y) (* x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

18.0ms	(* (cbrt (fma 4.0 (* t y) (* x x))) (cbrt (fma 4.0 (* t y) (* x x))))
1.0ms	(cbrt (fma 4.0 (* t y) (* x x)))
7.0ms	(cbrt (fma 4.0 (* t y) (* x x)))
1.0ms	(cbrt (fma 4.0 (* t y) (* x x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (cbrt (fma 4.0 (* t y) (* x x))) (cbrt (fma 4.0 (* t y) (* x x))))
275.0ms	(cbrt (fma 4.0 (* t y) (* x x)))
302.0ms	(cbrt (fma 4.0 (* t y) (* x x)))
298.0ms	(cbrt (fma 4.0 (* t y) (* x x)))

simplify5.2s

Counts

93 → 93

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	105	1734
1	234	1608
2	831	1473
3	4587	1274
done	5000	1274

prune729.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.3b

regimes949.0ms

Accuracy

0% (0.8b remaining)

Error of 6.1b against oracle of 5.2b and baseline of 6.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s

15725×

body

valid