Details

sample195.0ms

Algorithm

intervals

Results

59.0ms	47×	body	1280	valid
43.0ms	48×	body	10240	exit
25.0ms	50×	body	640	valid
13.0ms	118×	body	80	valid
8.0ms	28×	body	320	valid
8.0ms	104×	body	80	nan
3.0ms	9×	body	640	nan
3.0ms	11×	body	320	nan
3.0ms	13×	body	160	valid
1.0ms	1×	body	1280	nan
1.0ms	4×	body	160	nan

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4914
6	921
5	224
4	84
3	53
2	35
1	20
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.0b	(+ (- 1.0 y) (* y (exp z)))
2.2b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`times-frac`
11×	`associate-+l+`
9×	`prod-diff`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
5×	`fma-def` `add-cbrt-cube` `log-pow`
4×	`log-div` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-/r*` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`sum-log` `div-sub`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `associate-+l-` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 82

Calls

3 calls:

68.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
51.0ms	(+ (- 1.0 y) (* y (exp z)))
17.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series351.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
53.0ms	(+ (- 1.0 y) (* y (exp z)))
105.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify1.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1756
1	464
0	192

prune680.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (+ 1.0 (- (* (exp z) y) y))) t)
1.4b	(log (+ 1.0 (- (* (exp z) y) y)))
3.3b	(- (* (exp z) y) y)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`pow1`
6×	`add-exp-log`
5×	`add-cbrt-cube` `log-pow` `add-log-exp`
4×	`log-div` `log-prod` `associate-/l*`
3×	`expm1-log1p-u` `associate-/r*` `prod-diff` `log1p-expm1-u`
2×	`flip3-+` `div-sub` `flip-+`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `div-exp` `rem-log-exp` `div-inv` `flip--` `distribute-lft-out`

Counts

3 → 71

Calls

3 calls:

77.0ms	(/ (log (+ 1.0 (- (* (exp z) y) y))) t)
36.0ms	(log (+ 1.0 (- (* (exp z) y) y)))
17.0ms	(- (* (exp z) y) y)

series334.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(/ (log (+ 1.0 (- (* (exp z) y) y))) t)
63.0ms	(log (+ 1.0 (- (* (exp z) y) y)))
47.0ms	(- (* (exp z) y) y)

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1848
1	475
0	196

prune605.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y (expm1 z) 1.0)
0.0b	(/ (log (fma y (expm1 z) 1.0)) t)
3.3b	(log (fma y (expm1 z) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
8×	`pow1`
6×	`add-exp-log`
5×	`add-cbrt-cube` `log-pow`
4×	`associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-/r*` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `fma-udef` `div-inv`

Counts

3 → 57

Calls

3 calls:

1.0ms	(fma y (expm1 z) 1.0)
14.0ms	(/ (log (fma y (expm1 z) 1.0)) t)
2.0ms	(log (fma y (expm1 z) 1.0))

series422.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(fma y (expm1 z) 1.0)
245.0ms	(/ (log (fma y (expm1 z) 1.0)) t)
126.0ms	(log (fma y (expm1 z) 1.0))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
2	1261
1	339
0	149

prune487.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma y (expm1 z) 1.0))
0.0b	(/ (+ (log (sqrt (fma y (expm1 z) 1.0))) (log (sqrt (fma y (expm1 z) 1.0)))) t)
3.3b	(log (sqrt (fma y (expm1 z) 1.0)))
3.3b	(log (sqrt (fma y (expm1 z) 1.0)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

94×	`log-pow`
80×	`*-un-lft-identity`
78×	`times-frac`
73×	`pow1`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
40×	`distribute-rgt-out`
32×	`distribute-lft-out`
27×	`sqrt-pow1` `pow1/2`
26×	`associate-/l*`
12×	`log-prod`
9×	`sqrt-prod`
8×	`distribute-lft1-in` `distribute-rgt1-in` `add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `count-2` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 176

Calls

4 calls:

2.0ms	(sqrt (fma y (expm1 z) 1.0))
66.0ms	(/ (+ (log (sqrt (fma y (expm1 z) 1.0))) (log (sqrt (fma y (expm1 z) 1.0)))) t)
2.0ms	(log (sqrt (fma y (expm1 z) 1.0)))
2.0ms	(log (sqrt (fma y (expm1 z) 1.0)))

series4.1s

Counts

4 → 12

Calls

4 calls:

794.0ms	(sqrt (fma y (expm1 z) 1.0))
2.3s	(/ (+ (log (sqrt (fma y (expm1 z) 1.0))) (log (sqrt (fma y (expm1 z) 1.0)))) t)
488.0ms	(log (sqrt (fma y (expm1 z) 1.0)))
503.0ms	(log (sqrt (fma y (expm1 z) 1.0)))

simplify2.8s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
1	1246
0	449

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

regimes800.0ms

Accuracy

27% (5.4b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 11.1b

bsearch81.0ms

Steps

Iters	Range		Point
4	-5.841382810590438e-215	-2.9963158397475625e-215	-5.701067561750732e-215

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.8s	1481×	body	1280	valid
1.4s	1511×	body	10240	exit
958.0ms	3563×	body	80	valid
751.0ms	1495×	body	640	valid
305.0ms	898×	body	320	valid
241.0ms	2511×	body	80	nan
177.0ms	276×	body	640	nan
168.0ms	521×	body	160	valid
147.0ms	79×	body	2560	valid
53.0ms	101×	body	1280	nan
47.0ms	191×	body	320	nan
19.0ms	121×	body	160	nan