Details

sample123.0ms

Algorithm

intervals

Results

32.0ms	64×	body	10240	exit
30.0ms	51×	body	1280	valid
17.0ms	51×	body	640	valid
7.0ms	110×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	28×	body	320	valid
4.0ms	95×	body	80	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	640	nan
1.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan

simplify516.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (242.0ms)

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	533	10
12	535	10
done	535	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize9.0ms

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)
3.8b	(log (fma (expm1 z) y 1.0))

rewrite20.0ms

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:

9.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
3.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series251.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
124.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
60.0ms	(log (fma (expm1 z) y 1.0))

simplify733.0ms

Counts

124 → 124

Iterations

Useful iterations: done (729.0ms)

Iter	Nodes	Cost
0	252	4198
1	581	3760
2	1635	2551
done	5001	2542

prune331.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

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))
3.8b	(log (fma (expm1 z) y 1.0))

rewrite13.0ms

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:

2.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
8.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
1.0ms	(log (fma (expm1 z) y 1.0))

series247.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
119.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
62.0ms	(log (fma (expm1 z) y 1.0))

simplify1.9s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	189	1282
1	448	1075
2	1197	955
3	3621	935
done	5001	935

prune261.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (expm1 z) y 1.0))
0.1b	(cbrt (fma (expm1 z) y 1.0))
3.8b	(log (cbrt (fma (expm1 z) y 1.0)))
3.8b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 62

Calls

4 calls:

0.0ms	(cbrt (fma (expm1 z) y 1.0))
0.0ms	(cbrt (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)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (fma (expm1 z) y 1.0))
108.0ms	(cbrt (fma (expm1 z) y 1.0))
114.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
119.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify996.0ms

Counts

74 → 74

Iterations

Useful iterations: done (991.0ms)

Iter	Nodes	Cost
0	110	1166
1	262	1088
2	751	994
3	2712	946
done	5000	944

prune367.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* 2 (* 1/3 (log (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0)))) (/ 1 t))
0.1b	(cbrt (fma (expm1 z) y 1.0))
3.8b	(log (fma (expm1 z) y 1.0))
3.8b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log`
13×	`associate-r`
11×	`times-frac`
9×	`log-prod` `add-cbrt-cube`
8×	`pow1`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `log-pow` `unswap-sqr`
2×	`frac-times` `flip3-+` `pow1/3` `div-exp` `rem-log-exp` `associate-*l/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

29.0ms	(* (+ (* 2 (* 1/3 (log (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0)))) (/ 1 t))
0.0ms	(cbrt (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

522.0ms	(* (+ (* 2 (* 1/3 (log (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0)))) (/ 1 t))
111.0ms	(cbrt (fma (expm1 z) y 1.0))
63.0ms	(log (fma (expm1 z) y 1.0))
118.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify816.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (252.0ms)

Iter	Nodes	Cost
0	253	2180
1	651	1884
2	1961	1641
done	5000	1641

prune438.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.1b

regimes425.0ms

Accuracy

42.4% (4.1b remaining)

Error of 8.5b against oracle of 4.4b and baseline of 11.5b

bsearch63.0ms

Steps

Iters	Range		Point
5	-3.460978998595751e-79	-9.125160771875588e-80	-2.3067511430719193e-79

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	60
1	48	60
done	48	60

end0.0ms

sample3.3s

Algorithm

intervals

Results

811.0ms	1552×	body	10240	exit
785.0ms	1440×	body	1280	valid
491.0ms	1581×	body	640	valid
231.0ms	3486×	body	80	valid
186.0ms	946×	body	320	valid
139.0ms	106×	body	2560	valid
99.0ms	2566×	body	80	nan
56.0ms	268×	body	640	nan
55.0ms	459×	body	160	valid
35.0ms	111×	body	1280	nan
28.0ms	203×	body	320	nan
11.0ms	121×	body	160	nan