Details

sample109.0ms

Algorithm

intervals

Results

24.0ms	43×	body	10240	exit
23.0ms	46×	body	1280	valid
13.0ms	45×	body	640	valid
7.0ms	111×	body	80	valid
7.0ms	4×	body	2560	valid
6.0ms	34×	body	320	valid
2.0ms	71×	body	80	nan
2.0ms	16×	body	160	valid
2.0ms	8×	body	640	nan
1.0ms	3×	body	1280	nan
1.0ms	6×	body	320	nan
0.0ms	3×	body	160	nan

simplify217.0ms

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: 25.5b

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)
1.8b	(+ (- 1.0 y) (* y (exp z)))
1.9b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite117.0ms

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:

11.0ms	(* y (exp z))
51.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
33.0ms	(+ (- 1.0 y) (* y (exp z)))
18.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* y (exp z))
175.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
35.0ms	(+ (- 1.0 y) (* y (exp z)))
77.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (53.0ms)

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

prune371.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
20×	`pow1`
14×	`log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`log-prod` `flip3-+` `fma-neg` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate--r-` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

9.0ms	(* y (expm1 z))
19.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
24.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
7.0ms	(log (+ 1.0 (* y (expm1 z))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (expm1 z))
92.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
172.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
73.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify81.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	746	2869
1	2769	1983
2	5001	1785

prune558.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.0b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.0b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.0b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

94×	`log-pow`
80×	`*-un-lft-identity`
78×	`times-frac`
73×	`pow1`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
40×	`distribute-rgt-out`
32×	`distribute-lft-out`
27×	`sqrt-pow1` `pow1/2`
26×	`associate-/l*`
12×	`log-prod`
10×	`sqrt-div`
9×	`sqrt-prod`
8×	`add-exp-log` `log-div` `distribute-lft1-in` `distribute-rgt1-in`
6×	`flip3-+` `add-cbrt-cube` `flip-+`
4×	`expm1-log1p-u` `count-2` `div-sub` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`associate-+l-` `associate-+r-` `rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 186

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
55.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
5.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
5.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.8s

Counts

4 → 12

Calls

4 calls:

362.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.7s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
361.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
356.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	3093
1	5001	2585

prune635.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ t (sqrt (log (+ 1.0 (* y (expm1 z))))))
0.1b	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ t (sqrt (log (+ 1.0 (* y (expm1 z)))))))
3.0b	(log (+ 1.0 (* y (expm1 z))))
3.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

364×	`times-frac`
216×	`sqrt-prod`
186×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`pow1`
56×	`log-pow`
32×	`associate-/r*`
13×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`div-inv` `associate-/l*`
6×	`log-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `log-div` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `flip3-+` `rem-log-exp` `clear-num` `flip-+`
1×	`associate-/r/`

Counts

4 → 301

Calls

4 calls:

7.0ms	(/ t (sqrt (log (+ 1.0 (* y (expm1 z))))))
17.0ms	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ t (sqrt (log (+ 1.0 (* y (expm1 z)))))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ t (sqrt (log (+ 1.0 (* y (expm1 z))))))
163.0ms	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ t (sqrt (log (+ 1.0 (* y (expm1 z)))))))
80.0ms	(log (+ 1.0 (* y (expm1 z))))
79.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify128.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	938	6143
1	4621	5519
2	5001	5513

prune682.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

regimes326.0ms

Accuracy

39.7% (4.7b remaining)

Error of 8.4b against oracle of 3.7b and baseline of 11.5b

bsearch138.0ms

Steps

Iters	Range		Point
8	2.154642011990829e-105	1.2294377081901462e-100	1.5524150020171308e-104
7	-3.7288871600754755e-81	-2.016647678620738e-83	-4.412489822281961e-82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	32
1	48	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

750.0ms	1444×	body	1280	valid
701.0ms	1466×	body	10240	exit
435.0ms	1560×	body	640	valid
208.0ms	3496×	body	80	valid
168.0ms	958×	body	320	valid
94.0ms	78×	body	2560	valid
91.0ms	2501×	body	80	nan
51.0ms	495×	body	160	valid
48.0ms	255×	body	640	nan
28.0ms	101×	body	1280	nan
25.0ms	204×	body	320	nan
7.0ms	90×	body	160	nan