Details

sample102.0ms

Algorithm

intervals

Results

29.0ms	702×	body	80	nan
10.0ms	17×	body	1280	valid
9.0ms	180×	body	80	valid
8.0ms	26×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6
done	476	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.2b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.0b	(log (- 1.0 y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

14.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.0ms	(log (- 1.0 y))

series229.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* z (log (- 1.0 y)))
117.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
44.0ms	(log (- 1.0 y))

simplify105.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366
done	5001	366

prune200.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
80×	`times-frac`
76×	`*-un-lft-identity`
74×	`associate-r`
73×	`add-cube-cbrt`
56×	`unpow-prod-down`
51×	`prod-diff`
46×	`associate--l+`
34×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
21×	`pow1`
18×	`unswap-sqr`
13×	`log-pow`
12×	`log-prod`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
6×	`pow-to-exp` `associate-l` `pow-exp` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out--`
1×	`cbrt-undiv` `fma-neg` `diff-log` `fma-udef` `div-inv` `difference-of-squares`

Counts

4 → 233

Calls

4 calls:

68.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
36.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
36.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series446.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
125.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
167.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify137.0ms

Counts

245 → 245

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	936	3375
1	3893	2186
2	5001	2179
done	5001	2179

prune809.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
71×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
37×	`add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv`

Counts

3 → 132

Calls

3 calls:

0.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
37.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

series333.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
171.0ms	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify61.0ms

Counts

141 → 141

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	616	990
1	2555	827
2	5002	826
done	5002	826

prune514.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
76×	`add-sqr-sqrt`
71×	`associate-r`
56×	`unpow-prod-down`
40×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
11×	`prod-exp` `add-cbrt-cube`
9×	`pow1` `div-exp`
7×	`associate-l`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `flip3-+` `associate-*r/` `sum-log` `log-pow` `flip-+` `div-inv`

Counts

4 → 158

Calls

4 calls:

0.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
8.0ms	(+ (* (log y) x) (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))
35.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
8.0ms	(* (log y) x)

series414.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
179.0ms	(+ (* (log y) x) (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))
60.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
59.0ms	(* (log y) x)

simplify79.0ms

Counts

170 → 170

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	748	1165
1	3061	1015
2	5002	998
done	5002	998

prune593.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes178.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13
done	25	13

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	24123×	body	80	nan
272.0ms	5572×	body	80	valid
253.0ms	876×	body	640	valid
238.0ms	407×	body	1280	valid
125.0ms	742×	body	320	valid
46.0ms	436×	body	160	valid