Details

sample124.0ms

Algorithm

intervals

Results

35.0ms	64×	body	10240	exit
28.0ms	51×	body	1280	valid
16.0ms	51×	body	640	valid
7.0ms	110×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	28×	body	320	valid
3.0ms	95×	body	80	nan
1.0ms	7×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan

simplify249.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.5b	(+ (- 1.0 y) (* y (exp z)))
2.4b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
25.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
16.0ms	(+ (- 1.0 y) (* y (exp z)))
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
162.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
35.0ms	(+ (- 1.0 y) (* y (exp z)))
75.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune369.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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` `log-div`
5×	`add-cbrt-cube` `add-log-exp`
4×	`div-sub` `div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `flip3-+` `fma-neg` `associate-/r*` `flip-+` `log1p-expm1-u`
2×	`associate--r-` `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 → 121

Calls

3 calls:

10.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
8.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series308.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
153.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify70.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	677	2789
1	2374	1909
2	5001	1711

prune296.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
254×	`add-sqr-sqrt`
245×	`*-un-lft-identity`
240×	`add-cube-cbrt`
159×	`prod-diff`
49×	`pow1`
44×	`log-pow`
20×	`associate-/r*`
19×	`div-inv`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg`
2×	`log-div` `rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `diff-log` `rem-log-exp` `flip--` `flip-+` `inv-pow`

Counts

4 → 322

Calls

4 calls:

29.0ms	(- x (/ 1 (/ t (log (+ 1.0 (* y (expm1 z)))))))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
2.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- x (/ 1 (/ t (log (+ 1.0 (* y (expm1 z)))))))
77.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
195.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify105.0ms

Algorithm

egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1576	10340
1	5002	7401

prune529.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
3.8b	(log (+ 1.0 (* y (expm1 z))))
3.8b	(log (+ 1.0 (* y (expm1 z))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod` `log-prod`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `pow1/3` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 58

Calls

4 calls:

0.0ms	(cbrt t)
0.0ms	(cbrt t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt t)
215.0ms	(cbrt t)
106.0ms	(log (+ 1.0 (* y (expm1 z))))
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify93.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	236	420
1	782	376
2	3740	360
3	5001	358

prune336.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.0b

regimes442.0ms

Accuracy

44% (4.5b remaining)

Error of 8.9b against oracle of 4.4b and baseline of 12.4b

bsearch60.0ms

Steps

Iters	Range		Point
5	-3.460978998595751e-79	-9.125160771875588e-80	-2.3881342686465996e-79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample3.2s

Algorithm

intervals

Results

766.0ms	1552×	body	10240	exit
757.0ms	1440×	body	1280	valid
468.0ms	1581×	body	640	valid
206.0ms	3486×	body	80	valid
170.0ms	946×	body	320	valid
138.0ms	106×	body	2560	valid
94.0ms	2566×	body	80	nan
53.0ms	459×	body	160	valid
52.0ms	268×	body	640	nan
33.0ms	111×	body	1280	nan
26.0ms	203×	body	320	nan
10.0ms	121×	body	160	nan