Details

sample119.0ms

Algorithm

intervals

Results

26.0ms	47×	body	5120	exit
23.0ms	39×	body	1280	valid
21.0ms	55×	body	640	valid
8.0ms	114×	body	80	valid
7.0ms	6×	body	2560	valid
7.0ms	32×	body	320	valid
4.0ms	84×	body	80	nan
2.0ms	12×	body	160	valid
1.0ms	5×	body	640	nan
1.0ms	5×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	2×	body	160	nan

simplify215.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 24.0b

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)
1.7b	(log (+ (- 1.0 y) (* y (exp z))))
2.4b	(+ (- 1.0 y) (* y (exp z)))

rewrite29.0ms

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:

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

series297.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
158.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
76.0ms	(log (+ (- 1.0 y) (* y (exp z))))
41.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (53.0ms)

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

prune323.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 4.7b

Counts

115 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.2b	(log (+ 1.0 (* y (expm1 z))))

rewrite18.0ms

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:

5.0ms	(* y (expm1 z))
9.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series265.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* y (expm1 z))
154.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
74.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (41.0ms)

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

prune214.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 4.6b

Counts

86 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
2.2b	(log (+ 1.0 (* y (expm1 z))))

rewrite21.0ms

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:

3.0ms	(* y (expm1 z))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* y (expm1 z))
79.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
201.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify86.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	723	1701
1	3451	1541
2	5001	1448

prune352.0ms

Filtered

171 candidates to 101 candidates (59.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	170	9	179

Merged error: 4.6b

Counts

179 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.1b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
2.3b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
2.3b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite34.0ms

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:

3.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
16.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

363.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.5s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
345.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
351.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1260	3093
1	5001	2585

prune514.0ms

Filtered

198 candidates to 121 candidates (61.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	196	11	207

Merged error: 3.5b

Counts

207 → 11

regimes334.0ms

Accuracy

41.5% (4.5b remaining)

Error of 8.5b against oracle of 4.0b and baseline of 11.7b

bsearch71.0ms

Steps

Iters	Range		Point
6	-2.2112344662308785e-82	-3.0251522065951844e-83	-1.3110766951155834e-82

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample3.5s

Algorithm

intervals

Results

865.0ms	1540×	body	5120	exit
832.0ms	1448×	body	1280	valid
514.0ms	1511×	body	640	valid
252.0ms	3549×	body	80	valid
218.0ms	970×	body	320	valid
122.0ms	2589×	body	80	nan
79.0ms	66×	body	2560	valid
64.0ms	479×	body	160	valid
64.0ms	270×	body	640	nan
40.0ms	109×	body	1280	nan
33.0ms	190×	body	320	nan
12.0ms	115×	body	160	nan