Details

sample137.0ms

Algorithm

intervals

Results

57.0ms	776×	body	80	nan
12.0ms	179×	body	80	valid
12.0ms	15×	body	1280	valid
10.0ms	27×	body	640	valid
6.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid

simplify278.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	13
1	22	12
2	38	12
3	52	12
4	60	12
5	77	12
6	105	12
7	154	12
8	198	12
9	221	12
10	239	12
11	240	12
done	240	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.3b	(fma x (log y) (* z (log (- 1.0 y))))
4.7b	(log (- 1.0 y))

rewrite31.0ms

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:

16.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma x (log y) (* z (log (- 1.0 y))))
13.0ms	(log (- 1.0 y))

series238.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(* z (log (- 1.0 y)))
105.0ms	(fma x (log y) (* z (log (- 1.0 y))))
53.0ms	(log (- 1.0 y))

simplify3.7s

Counts

68 → 68

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	148	786
1	325	751
2	771	672
3	1745	655
4	4610	646
done	5000	645

prune386.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `distribute-rgt-in` `distribute-lft-in`
8×	`prod-diff`
7×	`associate-r` `associate-/r*`
6×	`log-prod` `associate-l` `associate--l+`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `pow-prod-down` `log-pow` `*-commutative` `unswap-sqr`
1×	`flip3--` `frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip--` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

84.0ms	(* y (+ 1.0 (/ 1/2 (/ (* 1.0 1.0) y))))
33.0ms	(* z (- (log 1.0) (* y (+ 1.0 (/ 1/2 (/ (* 1.0 1.0) y))))))
13.0ms	(/ 1/2 (/ (* 1.0 1.0) y))
0.0ms	(fma x (log y) (* z (- (log 1.0) (* y (+ 1.0 (/ 1/2 (/ (* 1.0 1.0) y)))))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* y (+ 1.0 (/ 1/2 (/ (* 1.0 1.0) y))))
143.0ms	(* z (- (log 1.0) (* y (+ 1.0 (/ 1/2 (/ (* 1.0 1.0) y))))))
23.0ms	(/ 1/2 (/ (* 1.0 1.0) y))
165.0ms	(fma x (log y) (* z (- (log 1.0) (* y (+ 1.0 (/ 1/2 (/ (* 1.0 1.0) y)))))))

simplify1.4s

Counts

137 → 137

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	250	2443
1	549	2341
2	1655	2006
done	5000	1968

prune800.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0)))))) (cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0)))))))
0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))

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:

23.0ms	(* (cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0)))))) (cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0)))))))
2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

459.0ms	(* (cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0)))))) (cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0)))))))
369.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
415.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
407.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))

simplify2.3s

Counts

93 → 93

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	187	4136
1	437	3876
2	1155	3549
3	3297	2943
done	5000	2806

prune710.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
0.6b	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
2.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

380.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
358.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
418.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))
396.0ms	(cbrt (fma (log y) x (* z (- (log 1.0) (* y (fma (/ 1/2 (* 1.0 1.0)) y 1.0))))))

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	100	2452
1	226	2396
2	567	2192
3	1631	1992
done	5000	1768

prune485.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes427.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	20	22
done	20	22

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.5s	24665×	body	80	nan
884.0ms	880×	body	640	valid
596.0ms	5640×	body	80	valid
573.0ms	673×	body	320	valid
471.0ms	409×	body	1280	valid
77.0ms	432×	body	160	valid