Details

sample168.0ms

Algorithm

intervals

Results

58.0ms	781×	body	80	nan
13.0ms	172×	body	80	valid
13.0ms	14×	body	1280	valid
12.0ms	29×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	17×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize14.0ms

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)))
0.3b	(fma x (log y) (* z (log (- 1.0 y))))
6.3b	(log (- 1.0 y))

rewrite40.0ms

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:

13.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
15.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma x (log y) (* z (log (- 1.0 y))))
7.0ms	(log (- 1.0 y))

series480.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
115.0ms	(* z (log (- 1.0 y)))
129.0ms	(fma x (log y) (* z (log (- 1.0 y))))
89.0ms	(log (- 1.0 y))

simplify1.0s

Counts

100 → 100

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	204	1528
1	488	1381
2	1552	1220
done	5000	1128

prune507.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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)))))
7.1b	(* z (pow y 2))

rewrite69.0ms

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:

13.0ms	(- (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))) t)
20.0ms	(- (* 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)))))
16.0ms	(* z (pow y 2))

series734.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(- (fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))) t)
184.0ms	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
198.0ms	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
37.0ms	(* z (pow y 2))

simplify1.6s

Counts

116 → 116

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	213	2952
1	545	2675
2	2119	2416
done	5000	2252

prune829.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.0b	(+ (* x (log y)) (- (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))) t))
0.3b	(* x (log y))
7.1b	(* z (pow y 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
33×	`add-sqr-sqrt`
26×	`prod-exp`
24×	`associate-r`
23×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
12×	`associate-+r+` `log-prod` `div-exp`
9×	`pow1` `associate-l` `prod-diff` `add-log-exp`
8×	`pow-to-exp` `times-frac` `pow-exp`
7×	`unpow-prod-down`
6×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative` `unpow2` `sqr-pow`
2×	`cbrt-undiv` `pow-prod-down` `sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `fma-def` `flip3-+` `diff-log` `associate-*r/` `associate--l+` `log-pow` `flip-+` `fma-udef` `div-inv`

Counts

4 → 134

Calls

4 calls:

32.0ms	(* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
37.0ms	(+ (* x (log y)) (- (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))) t))
9.0ms	(* x (log y))
16.0ms	(* z (pow y 2))

series485.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
290.0ms	(+ (* x (log y)) (- (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))) t))
72.0ms	(* x (log y))
41.0ms	(* z (pow y 2))

simplify1.8s

Counts

146 → 146

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	266	2439
1	672	2232
2	2599	1993
done	5001	1871

prune779.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)
7.1b	(* z (pow y 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
12.0ms	(* z (pow y 2))

series892.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt y)
269.0ms	(cbrt y)
268.0ms	(cbrt y)
62.0ms	(* z (pow y 2))

simplify3.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	74	457
1	156	422
2	558	371
3	3591	358
done	5001	358

prune494.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes304.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	36
1	31	36
done	31	36

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.0s	25084×	body	80	nan
548.0ms	5517×	body	80	valid
488.0ms	470×	body	160	valid
455.0ms	888×	body	640	valid
449.0ms	414×	body	1280	valid
276.0ms	749×	body	320	valid