Details

sample258.0ms

Algorithm

intervals

Results

108.0ms	784×	body	80	nan
18.0ms	178×	body	80	valid
16.0ms	27×	body	640	valid
15.0ms	13×	body	1280	valid
11.0ms	30×	body	320	valid
2.0ms	11×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	12	13
1	22	12
2	38	12
3	53	12
4	61	12
5	78	12
6	113	12
7	238	12
8	767	12
done	5000	12

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.0b	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
0.3b	(fma x (log y) (* z (log (- 1.0 y))))
5.8b	(log (- 1.0 y))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`log-prod`
9×	`prod-diff`
8×	`pow1`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg` `associate-l`
2×	`log-div` `flip3--` `log-pow` `flip--` `fma-udef`
1×	`sub-neg` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

30.0ms	(* z (log (- 1.0 y)))
13.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
1.0ms	(fma x (log y) (* z (log (- 1.0 y))))
13.0ms	(log (- 1.0 y))

series541.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* z (log (- 1.0 y)))
184.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
145.0ms	(fma x (log y) (* z (log (- 1.0 y))))
83.0ms	(log (- 1.0 y))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	204	1528
1	488	1381
2	1555	1220
done	5000	1128

prune923.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.2b	(fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
68×	`*-un-lft-identity`
63×	`add-cube-cbrt`
56×	`unpow-prod-down`
33×	`prod-diff`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`pow1`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
7×	`associate--l+` `log-pow`
6×	`pow-to-exp` `log-prod` `associate-l` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
2×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `fma-udef` `difference-of-squares`
1×	`cbrt-undiv` `diff-log` `div-inv`

Counts

4 → 210

Calls

4 calls:

79.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
59.0ms	(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
14.0ms	(- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
1.0ms	(fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series928.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
195.0ms	(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
373.0ms	(- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
254.0ms	(fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify3.3s

Counts

222 → 222

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	411	6086
1	1034	4745
2	4514	3826
done	5000	3822

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) t)
0.2b	(fma x (log y) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.2b	(* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.3b	(* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
93×	`prod-diff`
78×	`add-sqr-sqrt` `*-un-lft-identity`
66×	`add-cube-cbrt`
45×	`distribute-rgt-in` `distribute-lft-in`
25×	`pow1`
16×	`associate-r`
14×	`log-pow`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `flip3--` `flip3-+` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `fma-neg` `distribute-lft-out`
2×	`associate-l/` `-commutative` `fma-udef`
1×	`diff-log` `associate--l+` `unswap-sqr`

Counts

4 → 189

Calls

4 calls:

13.0ms	(- (fma x (log y) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) t)
1.0ms	(fma x (log y) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
81.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
200.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series3.0s

Counts

4 → 12

Calls

4 calls:

896.0ms	(- (fma x (log y) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) t)
810.0ms	(fma x (log y) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
383.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
908.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify1.0s

Counts

201 → 201

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	348	17203
1	1060	13485
done	5001	11608

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)) (cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
0.5b	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
0.5b	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
0.5b	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

90.0ms	(* (cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)) (cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
7.0ms	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
8.0ms	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
9.0ms	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))

series9.5s

Counts

4 → 12

Calls

4 calls:

2.4s	(* (cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)) (cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
2.7s	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
2.1s	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
2.3s	(cbrt (- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))

simplify1.3s

Counts

121 → 121

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	164	6211
1	379	5928
2	1382	5566
done	5000	4803

prune1.6s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	23
1	20	23
done	20	23

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.1s	23483×	body	80	nan
1.2s	5544×	body	80	valid
560.0ms	868×	body	640	valid
479.0ms	397×	body	1280	valid
366.0ms	779×	body	320	valid
98.0ms	443×	body	160	valid