Details

sample100.0ms

Algorithm

intervals

Results

32.0ms	741×	body	80	nan
11.0ms	169×	body	80	valid
10.0ms	15×	body	1280	valid
9.0ms	32×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	19×	body	160	valid

simplify211.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	13
1	22	12
2	37	12
3	47	12
4	55	12
5	72	12
6	103	12
7	149	12
8	189	12
9	212	12
10	233	12
11	237	12
done	237	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
0.0b	(* z (log (- 1.0 y)))
0.2b	(fma x (log y) (* z (log (- 1.0 y))))
5.7b	(log (- 1.0 y))

rewrite16.0ms

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:

3.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
7.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma x (log y) (* z (log (- 1.0 y))))
3.0ms	(log (- 1.0 y))

series279.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
67.0ms	(* z (log (- 1.0 y)))
81.0ms	(fma x (log y) (* z (log (- 1.0 y))))
43.0ms	(log (- 1.0 y))

simplify1.2s

Counts

100 → 100

Iterations

Useful iterations: 3 (493.0ms)

Iter	Nodes	Cost
0	204	1528
1	454	1378
2	1128	1221
3	3274	1115
done	5000	1115

prune310.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))) t)
0.0b	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.2b	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
7.4b	(* z (pow y 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`associate--l+`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
9×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
8×	`associate-r` `add-log-exp`
6×	`pow1` `log-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sub-neg` `unpow-prod-down` `fma-neg` `associate-*r/` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `associate-l` `prod-exp` `flip--`
2×	`diff-log` `log-pow` `frac-sub` `fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 104

Calls

4 calls:

3.0ms	(- (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))) t)
8.0ms	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.0ms	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
6.0ms	(* z (pow y 2))

series472.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(- (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))) t)
109.0ms	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
137.0ms	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
31.0ms	(* z (pow y 2))

simplify626.0ms

Counts

116 → 116

Iterations

Useful iterations: done (622.0ms)

Iter	Nodes	Cost
0	213	2952
1	504	2672
2	1543	2408
done	5001	2395

prune484.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2))) t)
0.0b	(* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)
0.2b	(fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)))
7.4b	(* z (pow y 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
28×	`add-sqr-sqrt`
25×	`prod-exp`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`associate-l` `add-cbrt-cube`
12×	`div-exp`
11×	`associate-r`
9×	`prod-diff`
8×	`pow-to-exp` `times-frac` `pow-exp`
7×	`unpow-prod-down`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `unpow2` `sqr-pow`
2×	`cbrt-undiv` `*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-*l/` `associate--l+` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

3.0ms	(- (fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2))) t)
15.0ms	(* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)
0.0ms	(fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)))
6.0ms	(* z (pow y 2))

series415.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(- (fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2))) t)
64.0ms	(* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)
128.0ms	(fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)))
35.0ms	(* z (pow y 2))

simplify645.0ms

Counts

124 → 124

Iterations

Useful iterations: done (641.0ms)

Iter	Nodes	Cost
0	209	2527
1	485	2297
2	1603	2038
done	5000	2029

prune465.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))))
7.4b	(* z (pow y 2))
7.4b	(* z (pow y 2))
7.4b	(* z (pow y 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`associate-l` `prod-exp`
6×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`pow1/3`

Counts

4 → 100

Calls

4 calls:

0.0ms	(cbrt (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))))
5.0ms	(* z (pow y 2))
5.0ms	(* z (pow y 2))
9.0ms	(* z (pow y 2))

series996.0ms

Counts

4 → 12

Calls

4 calls:

898.0ms	(cbrt (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))))
36.0ms	(* z (pow y 2))
30.0ms	(* z (pow y 2))
32.0ms	(* z (pow y 2))

simplify756.0ms

Counts

112 → 112

Iterations

Useful iterations: 3 (267.0ms)

Iter	Nodes	Cost
0	122	1281
1	258	1206
2	656	1037
3	1776	1027
done	5000	1027

prune574.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes250.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	29
1	25	29
done	25	29

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24144×	body	80	nan
276.0ms	5529×	body	80	valid
263.0ms	904×	body	640	valid
245.0ms	411×	body	1280	valid
129.0ms	736×	body	320	valid
47.0ms	444×	body	160	valid