Details

sample135.0ms

Algorithm

intervals

Results

38.0ms	48×	body	1280	valid
26.0ms	53×	body	640	valid
14.0ms	104×	body	80	valid
11.0ms	33×	body	320	valid
8.0ms	87×	body	80	nan
4.0ms	17×	body	160	valid
4.0ms	37×	body	80	overflowed
3.0ms	2×	body	2560	valid
3.0ms	9×	body	640	nan
3.0ms	10×	body	320	nan
3.0ms	5×	body	1280	nan
1.0ms	3×	body	160	nan

simplify216.0ms

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: 23.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
0.0b	(* y (exp z))
1.6b	(log (+ (- 1.0 y) (* y (exp z))))
2.9b	(+ (- 1.0 y) (* y (exp z)))

rewrite60.0ms

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:

23.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(* y (exp z))
12.0ms	(log (+ (- 1.0 y) (* y (exp z))))
17.0ms	(+ (- 1.0 y) (* y (exp z)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
22.0ms	(* y (exp z))
78.0ms	(log (+ (- 1.0 y) (* y (exp z))))
36.0ms	(+ (- 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

prune355.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.2b	(log (+ 1.0 (* y (expm1 z))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

3.0ms	(* y (expm1 z))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series272.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* y (expm1 z))
162.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	429	631
1	1711	580
2	5002	571

prune251.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.2b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.2b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 189

Calls

4 calls:

3.0ms	(* y (expm1 z))
33.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
2.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

38.0ms	(* y (expm1 z))
1.5s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
348.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
348.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1209	2963
1	5001	2509

prune627.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize19.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (+ 1.0 (* (* (cbrt (* y (expm1 z))) (cbrt (* y (expm1 z)))) (cbrt (* y (expm1 z))))))
13.6b	(cbrt (* y (expm1 z)))
13.6b	(cbrt (* y (expm1 z)))
13.6b	(cbrt (* y (expm1 z)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series593.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(log (+ 1.0 (* (* (cbrt (* y (expm1 z))) (cbrt (* y (expm1 z)))) (cbrt (* y (expm1 z))))))
98.0ms	(cbrt (* y (expm1 z)))
303.0ms	(cbrt (* y (expm1 z)))
103.0ms	(cbrt (* y (expm1 z)))

simplify97.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	266	668
1	796	583
2	3679	542
3	5001	541

prune244.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.8b

regimes202.0ms

Accuracy

42.7% (4.5b remaining)

Error of 8.3b against oracle of 3.8b and baseline of 11.6b

bsearch256.0ms

Steps

Iters	Range		Point
9	0.000431479263060677	213.0826250665956	210.72045394824104
8	4.678749619917463e-48	1.645067565017646e-43	1.1800524692053243e-46
4	-5.671731412597088e-76	-3.9419689679192305e-76	-4.718908347298701e-76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	47
1	70	47

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	1468×	body	1280	valid
750.0ms	1542×	body	640	valid
500.0ms	3568×	body	80	valid
302.0ms	906×	body	320	valid
228.0ms	2416×	body	80	nan
166.0ms	1529×	body	80	overflowed
126.0ms	85×	body	2560	valid
106.0ms	467×	body	160	valid
96.0ms	259×	body	640	nan
58.0ms	114×	body	1280	nan
55.0ms	210×	body	320	nan
20.0ms	110×	body	160	nan