Details

sample117.0ms

Algorithm

intervals

Results

33.0ms	64×	body	10240	exit
27.0ms	51×	body	1280	valid
16.0ms	51×	body	640	valid
6.0ms	110×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	28×	body	320	valid
3.0ms	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

simplify8.2s

Counts

1 → 1

Iterations

Useful iterations: 8 (113.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	77	12
5	105	12
6	139	12
7	186	12
8	299	10
9	469	10
10	600	10
11	649	10
12	936	10
13	3276	10
done	5000	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma y (expm1 z) 1.0)) t))
0.1b	(/ (log (fma y (expm1 z) 1.0)) t)
3.8b	(log (fma y (expm1 z) 1.0))

rewrite19.0ms

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:

10.0ms	(- x (/ (log (fma y (expm1 z) 1.0)) t))
3.0ms	(/ (log (fma y (expm1 z) 1.0)) t)
1.0ms	(log (fma y (expm1 z) 1.0))

series307.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(- x (/ (log (fma y (expm1 z) 1.0)) t))
151.0ms	(/ (log (fma y (expm1 z) 1.0)) t)
75.0ms	(log (fma y (expm1 z) 1.0))

simplify606.0ms

Counts

124 → 124

Iterations

Useful iterations: done (601.0ms)

Iter	Nodes	Cost
0	262	4232
1	609	3791
2	1851	2579
done	5000	2569

prune314.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (* (log (fma y (expm1 z) 1.0)) (/ 1 t)))
0.1b	(* (log (fma y (expm1 z) 1.0)) (/ 1 t))
3.8b	(log (fma y (expm1 z) 1.0))

rewrite14.0ms

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:

3.0ms	(- x (* (log (fma y (expm1 z) 1.0)) (/ 1 t)))
9.0ms	(* (log (fma y (expm1 z) 1.0)) (/ 1 t))
1.0ms	(log (fma y (expm1 z) 1.0))

series309.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- x (* (log (fma y (expm1 z) 1.0)) (/ 1 t)))
156.0ms	(* (log (fma y (expm1 z) 1.0)) (/ 1 t))
75.0ms	(log (fma y (expm1 z) 1.0))

simplify645.0ms

Counts

82 → 82

Iterations

Useful iterations: done (643.0ms)

Iter	Nodes	Cost
0	199	1316
1	476	1106
2	1537	983
done	5001	982

prune240.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma y (expm1 z) 1.0))
0.1b	(cbrt (fma y (expm1 z) 1.0))
3.8b	(log (cbrt (fma y (expm1 z) 1.0)))
3.8b	(log (cbrt (fma y (expm1 z) 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 y (expm1 z) 1.0))
0.0ms	(cbrt (fma y (expm1 z) 1.0))
1.0ms	(log (cbrt (fma y (expm1 z) 1.0)))
1.0ms	(log (cbrt (fma y (expm1 z) 1.0)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (fma y (expm1 z) 1.0))
157.0ms	(cbrt (fma y (expm1 z) 1.0))
139.0ms	(log (cbrt (fma y (expm1 z) 1.0)))
144.0ms	(log (cbrt (fma y (expm1 z) 1.0)))

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	110	1166
1	262	1088
2	779	994
3	3393	946
done	5000	944

prune349.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

32.0ms	(* (+ (* 2 (* 1/3 (log (fma y (expm1 z) 1.0)))) (log (cbrt (fma y (expm1 z) 1.0)))) (/ 1 t))
0.0ms	(cbrt (fma y (expm1 z) 1.0))
1.0ms	(log (fma y (expm1 z) 1.0))
1.0ms	(log (cbrt (fma y (expm1 z) 1.0)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (+ (* 2 (* 1/3 (log (fma y (expm1 z) 1.0)))) (log (cbrt (fma y (expm1 z) 1.0)))) (/ 1 t))
155.0ms	(cbrt (fma y (expm1 z) 1.0))
77.0ms	(log (fma y (expm1 z) 1.0))
145.0ms	(log (cbrt (fma y (expm1 z) 1.0)))

simplify771.0ms

Counts

99 → 99

Iterations

Useful iterations: done (768.0ms)

Iter	Nodes	Cost
0	263	2214
1	679	1915
2	2320	1670
done	5000	1669

prune437.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

regimes316.0ms

Accuracy

42.5% (4.1b remaining)

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

bsearch61.0ms

Steps

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.1s

Algorithm

intervals

Results

761.0ms	1552×	body	10240	exit
750.0ms	1440×	body	1280	valid
454.0ms	1581×	body	640	valid
202.0ms	3486×	body	80	valid
174.0ms	946×	body	320	valid
137.0ms	106×	body	2560	valid
97.0ms	2566×	body	80	nan
52.0ms	268×	body	640	nan
50.0ms	459×	body	160	valid
39.0ms	111×	body	1280	nan
26.0ms	203×	body	320	nan
10.0ms	121×	body	160	nan