Details

sample103.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
19.0ms	43×	body	10240	exit
17.0ms	65×	body	640	valid
6.0ms	103×	body	80	valid
5.0ms	4×	body	2560	valid
5.0ms	28×	body	320	valid
4.0ms	9×	body	640	nan
2.0ms	65×	body	80	nan
2.0ms	17×	body	160	valid
1.0ms	4×	body	1280	nan
1.0ms	6×	body	320	nan
0.0ms	4×	body	160	nan

simplify207.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

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	(log (+ (- 1.0 y) (* y (exp z))))
2.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite118.0ms

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))
52.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
19.0ms	(log (+ (- 1.0 y) (* y (exp z))))
33.0ms	(+ (- 1.0 y) (* y (exp z)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
164.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
73.0ms	(log (+ (- 1.0 y) (* y (exp z))))
40.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune356.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* y (expm1 z)))
0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.6b	(log (+ 1.0 (* y (expm1 z))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

8.0ms	(+ 1.0 (* y (expm1 z)))
7.0ms	(* y (expm1 z))
13.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ 1.0 (* y (expm1 z)))
58.0ms	(* y (expm1 z))
171.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	473	718
1	1893	652
2	5001	644

prune302.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.2b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.6b	(log (+ 1.0 (* y (expm1 z))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
67×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
24×	`pow1`
20×	`add-exp-log` `associate-/r*`
17×	`log-pow`
13×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l`
2×	`log-div` `rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

7.0ms	(* y (expm1 z))
5.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
10.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* y (expm1 z))
211.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
84.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
80.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify80.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	723	1701
1	3451	1541
2	5002	1448

prune413.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
3.6b	(log (+ 1.0 (* y (expm1 z))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

541×	`times-frac`
249×	`add-sqr-sqrt`
247×	`add-cube-cbrt` `*-un-lft-identity`
54×	`pow1`
51×	`add-exp-log`
47×	`log-pow`
34×	`div-exp`
33×	`div-inv`
20×	`associate-/r*` `add-cbrt-cube`
16×	`associate-/l*`
9×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l`
2×	`log-div` `frac-2neg` `clear-num`
1×	`pow-flip` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `inv-pow` `unswap-sqr`

Counts

4 → 344

Calls

4 calls:

7.0ms	(* y (expm1 z))
9.0ms	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
19.0ms	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series694.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (expm1 z))
482.0ms	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
89.0ms	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
83.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify72.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1562	4934
1	5001	4359

prune876.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

regimes367.0ms

Accuracy

40.9% (4.0b remaining)

Error of 8.6b against oracle of 4.6b and baseline of 11.4b

bsearch46.0ms

Steps

Iters	Range		Point
5	-3.087949021713197e-106	-1.0243182995054909e-106	-1.8224838885264432e-106

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	36	16
2	36	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

725.0ms	1432×	body	1280	valid
711.0ms	1518×	body	10240	exit
432.0ms	1568×	body	640	valid
200.0ms	3512×	body	80	valid
159.0ms	935×	body	320	valid
86.0ms	71×	body	2560	valid
81.0ms	2521×	body	80	nan
58.0ms	509×	body	160	valid
51.0ms	280×	body	640	nan
30.0ms	110×	body	1280	nan
26.0ms	193×	body	320	nan
8.0ms	101×	body	160	nan