Details

sample101.0ms

Algorithm

intervals

Results

27.0ms	45×	body	10240	exit
22.0ms	43×	body	1280	valid
16.0ms	57×	body	640	valid
8.0ms	130×	body	80	valid
3.0ms	80×	body	80	nan
2.0ms	14×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	7×	body	640	nan
1.0ms	4×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	3×	body	160	nan

simplify738.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (291.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	77	12
5	105	12
6	137	12
7	176	12
8	217	12
9	280	12
10	470	10
11	558	10
12	562	10
done	562	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
5.0b	(log (fma (expm1 z) y 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

0.0ms	(fma (expm1 z) y 1.0)
3.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
1.0ms	(log (fma (expm1 z) y 1.0))

series308.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(fma (expm1 z) y 1.0)
161.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
87.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

66 → 66

Iterations

Useful iterations: 3 (575.0ms)

Iter	Nodes	Cost
0	146	855
1	308	819
2	838	747
3	2412	737
done	5000	737

prune269.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (fma (expm1 z) y 1.0))
0.2b	(sqrt (fma (expm1 z) y 1.0))
4.8b	(log (sqrt (fma (expm1 z) y 1.0)))
4.8b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `log-prod` `sqrt-prod`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 68

Calls

4 calls:

1.0ms	(sqrt (fma (expm1 z) y 1.0))
1.0ms	(sqrt (fma (expm1 z) y 1.0))
1.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
1.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (fma (expm1 z) y 1.0))
114.0ms	(sqrt (fma (expm1 z) y 1.0))
178.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
174.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify941.0ms

Counts

80 → 80

Iterations

Useful iterations: done (938.0ms)

Iter	Nodes	Cost
0	208	1884
1	589	1694
2	2177	1576
done	5001	1550

prune403.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* 1/2 (log (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
0.2b	(sqrt (fma (expm1 z) y 1.0))
4.8b	(log (sqrt (fma (expm1 z) y 1.0)))
5.0b	(log (fma (expm1 z) y 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
16×	`log-pow`
12×	`pow1`
10×	`pow1/2`
9×	`log-prod`
8×	`add-exp-log` `distribute-rgt-out`
6×	`sqrt-pow1` `sqrt-prod` `add-cbrt-cube` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/r*`
2×	`rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

14.0ms	(/ (+ (* 1/2 (log (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
1.0ms	(sqrt (fma (expm1 z) y 1.0))
6.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
1.0ms	(log (fma (expm1 z) y 1.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

826.0ms	(/ (+ (* 1/2 (log (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
115.0ms	(sqrt (fma (expm1 z) y 1.0))
180.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
80.0ms	(log (fma (expm1 z) y 1.0))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	376	2446
1	1010	2212
2	3528	2035
done	5000	2022

prune530.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (expm1 z) y 1.0))
4.8b	(log (sqrt (fma (expm1 z) y 1.0)))
4.9b	(log (cbrt (fma (expm1 z) y 1.0)))
4.9b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
8×	`pow1`
7×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `rem-log-exp` `sqrt-prod`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt (fma (expm1 z) y 1.0))
1.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (fma (expm1 z) y 1.0))
177.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
167.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
160.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify882.0ms

Counts

80 → 80

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	241	1526
1	660	1410
2	2323	1293
done	5001	1286

prune455.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes341.0ms

Accuracy

42.2% (4.0b remaining)

Error of 8.4b against oracle of 4.4b and baseline of 11.3b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	86
1	55	86
done	55	86

end0.0ms

sample3.3s

Algorithm

intervals

Results

793.0ms	1518×	body	10240	exit
778.0ms	1447×	body	1280	valid
468.0ms	1590×	body	640	valid
212.0ms	3550×	body	80	valid
169.0ms	879×	body	320	valid
113.0ms	87×	body	2560	valid
99.0ms	2609×	body	80	nan
58.0ms	292×	body	640	nan
57.0ms	466×	body	160	valid
37.0ms	126×	body	1280	nan
27.0ms	203×	body	320	nan
9.0ms	103×	body	160	nan