Details

sample111.0ms

Algorithm

intervals

Results

29.0ms	47×	body	1280	valid
20.0ms	58×	body	640	valid
12.0ms	114×	body	80	valid
5.0ms	3×	body	2560	valid
5.0ms	22×	body	320	valid
4.0ms	80×	body	80	nan
3.0ms	11×	body	640	nan
3.0ms	49×	body	80	overflowed
2.0ms	6×	body	1280	nan
2.0ms	13×	body	160	valid
1.0ms	5×	body	320	nan
1.0ms	6×	body	160	nan

simplify234.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 24.6b

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)
2.2b	(+ (- 1.0 y) (* y (exp z)))
2.5b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite27.0ms

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)))
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* y (exp z))
50.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
11.0ms	(+ (- 1.0 y) (* y (exp z)))
14.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify56.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

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

prune190.0ms

Filtered

92 candidates to 68 candidates (26.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 5.3b

Counts

93 → 5

localize12.0ms

Local error

Found 2 expressions with local error:

3.1b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.5b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

2 → 51

Calls

2 calls:

7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
6.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series47.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
31.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	308	605
1	1387	547
2	5001	542

prune229.0ms

Filtered

57 candidates to 45 candidates (21.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	52	10	62

Merged error: 5.3b

Counts

62 → 10

localize24.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
3.1b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.7b	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `associate-/r*`
12×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
6×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

3 → 135

Calls

3 calls:

7.0ms	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
8.0ms	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

series87.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
13.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
44.0ms	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	623	2108
1	3184	1929
2	5001	1843

prune247.0ms

Filtered

144 candidates to 81 candidates (43.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	144	10	154

Merged error: 5.3b

Counts

154 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

3.1b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
21.5b	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
21.5b	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
21.5b	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
2.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
2.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
3.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
46.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
45.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
46.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	374	1161
1	1546	1097
2	5002	1007

prune479.0ms

Filtered

73 candidates to 58 candidates (20.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	73	10	83

Merged error: 5.3b

Counts

83 → 10

regimes1.3s

Accuracy

71% (4.6b remaining)

Error of 9.3b against oracle of 4.7b and baseline of 20.5b

bsearch180.0ms

Steps

Iters	Range		Point
7	-2.099185052842988e-192	-8.923574605892771e-195	-1.0341348539470992e-192
9	-3.3107726262830282e-56	-5.946363912233483e-65	-1.6801811259133204e-60
9	-4579.616410621801	-0.0182618413943067	-0.01853572616853024

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	35
1	59	35

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	1498×	body	1280	valid
673.0ms	1570×	body	640	valid
316.0ms	3546×	body	80	valid
239.0ms	866×	body	320	valid
154.0ms	89×	body	2560	valid
146.0ms	2444×	body	80	nan
104.0ms	1529×	body	80	overflowed
82.0ms	454×	body	160	valid
79.0ms	250×	body	640	nan
47.0ms	97×	body	1280	nan
47.0ms	213×	body	320	nan
18.0ms	124×	body	160	nan

Details

sample111.0ms

simplify234.0ms

prune4.0ms

localize10.0ms

rewrite27.0ms

series80.0ms

simplify56.0ms

prune190.0ms

localize12.0ms

rewrite14.0ms

series47.0ms

simplify45.0ms

prune229.0ms

localize24.0ms

rewrite27.0ms

series87.0ms

simplify84.0ms

prune247.0ms

localize16.0ms

rewrite15.0ms

series151.0ms

simplify49.0ms

prune479.0ms

regimes1.3s

bsearch180.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling