Details

sample173.0ms

Algorithm

intervals

Results

47.0ms	41×	body	10240	exit
33.0ms	45×	body	1280	valid
20.0ms	43×	body	640	valid
12.0ms	121×	body	80	valid
10.0ms	32×	body	320	valid
6.0ms	2×	body	2560	valid
6.0ms	83×	body	80	nan
5.0ms	14×	body	640	nan
3.0ms	14×	body	160	valid
2.0ms	7×	body	320	nan
0.0ms	1×	body	1280	nan
0.0ms	1×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 10 (529.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	53	12
4	77	12
5	106	12
6	138	12
7	176	12
8	232	12
9	295	12
10	459	10
11	498	10
12	500	10
done	500	10

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.3b	(log (fma (expm1 z) y 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 115

Calls

3 calls:

24.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
8.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
2.0ms	(log (fma (expm1 z) y 1.0))

series479.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
250.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
112.0ms	(log (fma (expm1 z) y 1.0))

simplify1.7s

Counts

124 → 124

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	252	4198
1	580	3760
2	1528	2551
done	5001	2111

prune520.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
3.3b	(log (fma (expm1 z) y 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
5×	`add-log-exp`
4×	`associate-l` `prod-exp`
3×	`expm1-log1p-u` `log-prod` `fma-neg` `prod-diff` `log1p-expm1-u` `unswap-sqr`
2×	`div-exp` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `div-inv`

Counts

3 → 73

Calls

3 calls:

12.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
32.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
3.0ms	(log (fma (expm1 z) y 1.0))

series418.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
189.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
95.0ms	(log (fma (expm1 z) y 1.0))

simplify3.1s

Counts

82 → 82

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	189	1282
1	442	1075
2	1147	955
3	3218	936
done	5000	902

prune355.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1 x (- (/ (log (fma (expm1 z) y 1.0)) t)))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.3b	(log (fma (expm1 z) y 1.0))

rewrite24.0ms

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 1 x (- (/ (log (fma (expm1 z) y 1.0)) t)))
18.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series380.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(fma 1 x (- (/ (log (fma (expm1 z) y 1.0)) t)))
189.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
81.0ms	(log (fma (expm1 z) y 1.0))

simplify2.0s

Counts

66 → 66

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	145	925
1	298	878
2	766	784
3	2055	781
done	5000	776

prune292.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
3.3b	(log (fma (expm1 z) y 1.0))
3.3b	(log (fma (expm1 z) y 1.0))
3.3b	(log (fma (expm1 z) y 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 69

Calls

4 calls:

6.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))

series811.0ms

Counts

4 → 12

Calls

4 calls:

520.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
86.0ms	(log (fma (expm1 z) y 1.0))
105.0ms	(log (fma (expm1 z) y 1.0))
101.0ms	(log (fma (expm1 z) y 1.0))

simplify903.0ms

Counts

81 → 81

Iterations

Useful iterations: done (899.0ms)

Iter	Nodes	Cost
0	197	1445
1	458	1353
2	1337	1229
done	5000	1180

prune556.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.4b

regimes783.0ms

Accuracy

43.9% (3.8b remaining)

Error of 8.4b against oracle of 4.6b and baseline of 11.3b

bsearch131.0ms

Steps

Iters	Range		Point
8	-8.638556380710241e-134	-2.110475534095123e-136	-6.310119903545574e-134

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	33	33
done	33	33

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.5s	1557×	body	10240	exit
1.4s	1443×	body	1280	valid
879.0ms	3558×	body	80	valid
766.0ms	1545×	body	640	valid
540.0ms	84×	body	2560	valid
397.0ms	915×	body	320	valid
156.0ms	2431×	body	80	nan
91.0ms	478×	body	160	valid
90.0ms	263×	body	640	nan
75.0ms	195×	body	320	nan
56.0ms	110×	body	1280	nan
14.0ms	100×	body	160	nan