Details

sample4.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 28.166482%

Results

255.0ms	52×	body	640	valid
22.0ms	38×	body	1280	valid
9.0ms	120×	body	80	valid
5.0ms	26×	body	320	valid
3.0ms	11×	body	640	nan
3.0ms	48×	body	80	overflowed
2.0ms	18×	body	160	valid
2.0ms	2×	body	2560	valid
2.0ms	34×	body	80	nan
0.0ms	3×	body	160	nan
0.0ms	2×	body	320	nan
0.0ms	1×	body	80	invalid

simplify214.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	628	7
9	935	7
10	1028	7
11	1354	7
12	3968	7
13	5002	7

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 22.9b

Counts

2 → 1

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)
2.0b	(+ (- 1.0 y) (* y (exp z)))
2.2b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `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` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
6.0ms	(+ (- 1.0 y) (* y (exp z)))
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* y (exp z))
41.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
7.0ms	(+ (- 1.0 y) (* y (exp z)))
15.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify50.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5002	726

prune170.0ms

Filtered

68 candidates to 92 candidates (-35.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 4.0b

Counts

93 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 (pow z 2)) z)
0.1b	(/ (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))) t)
2.8b	(* y (+ (* 1/2 (pow z 2)) z))
5.1b	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`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×	`log-div` `flip3-+` `flip-+` `associate-/l*`
3×	`log-prod` `associate-r` `associate-l` `associate-/r*`
2×	`div-sub` `associate-*r/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(+ (* 1/2 (pow z 2)) z)
5.0ms	(/ (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))) t)
7.0ms	(* y (+ (* 1/2 (pow z 2)) z))
2.0ms	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* 1/2 (pow z 2)) z)
41.0ms	(/ (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))) t)
13.0ms	(* y (+ (* 1/2 (pow z 2)) z))
20.0ms	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	459	879
1	1787	805
2	5001	800

prune203.0ms

Filtered

66 candidates to 92 candidates (-39.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Merged error: 4.0b

Counts

99 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 (pow z 2)) z)
0.1b	(* (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))) (/ 1 t))
2.8b	(* y (+ (* 1/2 (pow z 2)) z))
5.1b	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`add-exp-log` `-un-lft-identity` `associate-r*`
15×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
10×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
5×	`prod-exp`
4×	`unswap-sqr`
3×	`log-prod` `flip3-+` `associate-*r/` `cbrt-unprod` `flip-+`
2×	`log-div` `div-exp` `pow-prod-down` `log-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `rem-log-exp` `sum-log` `un-div-inv` `div-inv`

Counts

4 → 84

Calls

4 calls:

5.0ms	(+ (* 1/2 (pow z 2)) z)
9.0ms	(* (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))) (/ 1 t))
7.0ms	(* y (+ (* 1/2 (pow z 2)) z))
3.0ms	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* 1/2 (pow z 2)) z)
42.0ms	(* (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))) (/ 1 t))
12.0ms	(* y (+ (* 1/2 (pow z 2)) z))
18.0ms	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

simplify64.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	547	866
1	2297	762
2	5001	750

prune198.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 4.0b

Counts

105 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))))
0.3b	(/ 1 (/ t (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))))
2.8b	(* y (+ (* 1/2 (pow z 2)) z))
5.1b	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

rewrite27.0ms

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` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l`
2×	`log-div` `rec-exp` `frac-2neg` `flip3-+` `1-exp` `associate-*r/` `clear-num` `flip-+`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

3.0ms	(/ t (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))))
7.0ms	(* y (+ (* 1/2 (pow z 2)) z))
2.0ms	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ t (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z)))))
30.0ms	(/ 1 (/ t (log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))))
13.0ms	(* y (+ (* 1/2 (pow z 2)) z))
19.0ms	(log (+ 1.0 (* y (+ (* 1/2 (pow z 2)) z))))

simplify87.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	744	2100
1	3416	1918
2	5002	1830

prune236.0ms

Filtered

92 candidates to 167 candidates (-81.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	167	10	177

Merged error: 4.0b

Counts

177 → 10

regimes1000.0ms

Accuracy

77.5% (4.4b remaining)

Error of 8.5b against oracle of 4.1b and baseline of 23.5b

bsearch92.0ms

Steps

Iters	Range		Point
7	5.025565432032554e-208	2.128466918886463e-206	1.996635223084275e-206
6	-0.0007847244422099917	-0.00018390156386416634	-0.00040011550032981527

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	26
1	54	26

end0.0ms

sample6.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 28.166482%

Results

809.0ms	1392×	body	1280	valid
515.0ms	1522×	body	640	valid
270.0ms	3617×	body	80	valid
203.0ms	882×	body	320	valid
97.0ms	75×	body	2560	valid
95.0ms	1514×	body	80	overflowed
70.0ms	512×	body	160	valid
64.0ms	256×	body	640	nan
54.0ms	1044×	body	80	nan
41.0ms	107×	body	1280	nan
33.0ms	202×	body	320	nan
12.0ms	110×	body	160	nan
1.0ms	27×	body	80	invalid

Details

sample4.2s

simplify214.0ms

prune4.0ms

localize10.0ms

rewrite26.0ms

series68.0ms

simplify50.0ms

prune170.0ms

localize12.0ms

rewrite21.0ms

series79.0ms

simplify53.0ms

prune203.0ms

localize14.0ms

rewrite27.0ms

series78.0ms

simplify64.0ms

prune198.0ms

localize13.0ms

rewrite27.0ms

series135.0ms

simplify87.0ms

prune236.0ms

regimes1000.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling