Details

sample93.0ms

Algorithm

intervals

Results

24.0ms	49×	body	10240	exit
16.0ms	33×	body	1280	valid
12.0ms	41×	body	640	valid
8.0ms	129×	body	80	valid
5.0ms	30×	body	320	valid
2.0ms	68×	body	80	nan
2.0ms	22×	body	160	valid
2.0ms	2×	body	2560	valid
2.0ms	11×	body	640	nan
1.0ms	5×	body	320	nan
0.0ms	4×	body	160	nan

simplify217.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
3.2b	(log (+ (- 1.0 y) (* y (exp z))))
3.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite59.0ms

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))
24.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
17.0ms	(+ (- 1.0 y) (* y (exp z)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
153.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
77.0ms	(log (+ (- 1.0 y) (* y (exp z))))
64.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

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

prune413.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

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)
4.9b	(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))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series316.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
160.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify76.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (54.0ms)

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

prune326.0ms

Filtered

130 candidates to 73 candidates (56.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ 1 (/ t (log (+ 1.0 (* y (expm1 z)))))))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
4.9b	(log (+ 1.0 (* y (expm1 z))))

rewrite66.0ms

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:

28.0ms	(- x (/ 1 (/ t (log (+ 1.0 (* y (expm1 z)))))))
2.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
9.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- x (/ 1 (/ t (log (+ 1.0 (* y (expm1 z)))))))
209.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
80.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
79.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify105.0ms

Algorithm

egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1576	10340
1	5001	7401

prune594.0ms

Filtered

334 candidates to 127 candidates (38.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z)))))))
0.1b	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
0.1b	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
4.9b	(log (+ 1.0 (* y (expm1 z))))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

2086×	`times-frac`
1145×	`add-sqr-sqrt`
1118×	`*-un-lft-identity`
1110×	`add-cube-cbrt`
639×	`prod-diff`
169×	`pow1`
164×	`log-pow`
123×	`div-inv`
49×	`add-exp-log`
34×	`div-exp`
20×	`associate-/r*`
18×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`difference-of-squares`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg`
2×	`log-div` `frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `diff-log` `rem-log-exp` `flip--` `flip-+` `associate-/l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 991

Calls

4 calls:

101.0ms	(- x (/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z)))))))
13.0ms	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
3.0ms	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series930.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z)))))))
82.0ms	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
682.0ms	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
85.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify410.0ms

Algorithm

egg-herbie

Counts

1003 → 1003

Iterations

Useful iterations: 1 (77.0ms)

Iter	Nodes	Cost
0	4504	46002
1	5001	41242

prune1.9s

Filtered

1003 candidates to 356 candidates (35.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes423.0ms

Accuracy

46.4% (3.8b remaining)

Error of 8.1b against oracle of 4.3b and baseline of 11.3b

bsearch109.0ms

Steps

Iters	Range		Point
7	3.6655384296299976e-81	3.6842556330088986e-79	1.5498352032466958e-79
4	-8.290114156802151e-76	-4.391269012775651e-76	-5.25661220139478e-76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	15
1	37	15

end0.0ms

sample3.1s

Algorithm

intervals

Results

752.0ms	1413×	body	1280	valid
731.0ms	1491×	body	10240	exit
466.0ms	1590×	body	640	valid
220.0ms	3573×	body	80	valid
164.0ms	892×	body	320	valid
94.0ms	2479×	body	80	nan
75.0ms	60×	body	2560	valid
59.0ms	275×	body	640	nan
56.0ms	496×	body	160	valid
31.0ms	107×	body	1280	nan
25.0ms	190×	body	320	nan
9.0ms	113×	body	160	nan