Details

sample89.0ms

Algorithm

intervals

Results

23.0ms	41×	body	1280	valid
14.0ms	44×	body	640	valid
9.0ms	38×	body	320	valid
8.0ms	116×	body	80	valid
6.0ms	5×	body	2560	valid
4.0ms	92×	body	80	nan
2.0ms	37×	body	80	overflowed
2.0ms	14×	body	160	valid
1.0ms	3×	body	1280	nan
1.0ms	4×	body	640	nan
1.0ms	4×	body	320	nan
1.0ms	5×	body	160	nan

simplify220.0ms

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: 24.1b

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)
1.8b	(log (+ (- 1.0 y) (* y (exp z))))
2.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite31.0ms

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:

8.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
156.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
76.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

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

prune329.0ms

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: 4.4b

Counts

115 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
20×	`pow1`
14×	`log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`log-prod` `flip3-+` `fma-neg` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate--r-` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

8.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
3.0ms	(* y (expm1 z))
5.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
41.0ms	(* y (expm1 z))
151.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
78.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify82.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	746	2869
1	2769	1983
2	5001	1785

prune324.0ms

Filtered

153 candidates to 89 candidates (58.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	8	153
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	151	8	159

Merged error: 4.2b

Counts

159 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
2.7b	(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))
3.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* y (expm1 z))
200.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
80.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify126.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (99.0ms)

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

prune366.0ms

Filtered

171 candidates to 102 candidates (59.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	170	9	179

Merged error: 4.2b

Counts

179 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
2.7b	(log (cbrt (+ 1.0 (* y (expm1 z)))))
2.7b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
163.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
151.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
145.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	318	880
1	1062	820
2	5001	794

prune351.0ms

Filtered

82 candidates to 76 candidates (92.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 4.2b

Counts

91 → 9

regimes303.0ms

Accuracy

32.3% (4.8b remaining)

Error of 9.1b against oracle of 4.3b and baseline of 11.4b

bsearch57.0ms

Steps

Iters	Range		Point
6	-32116549.452598076	-3141188.981794727	-3197164.2606992587

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	30
1	38	30

end0.0ms

sample2.8s

Algorithm

intervals

Results

844.0ms	1435×	body	1280	valid
547.0ms	1599×	body	640	valid
254.0ms	3517×	body	80	valid
202.0ms	905×	body	320	valid
132.0ms	100×	body	2560	valid
118.0ms	2474×	body	80	nan
83.0ms	1521×	body	80	overflowed
69.0ms	284×	body	640	nan
66.0ms	474×	body	160	valid
40.0ms	111×	body	1280	nan
31.0ms	181×	body	320	nan
12.0ms	111×	body	160	nan

Details

sample89.0ms

simplify220.0ms

prune3.0ms

localize10.0ms

rewrite31.0ms

series288.0ms

simplify60.0ms

prune329.0ms

localize13.0ms

rewrite24.0ms

series352.0ms

simplify82.0ms

prune324.0ms

localize10.0ms

rewrite21.0ms

series405.0ms

simplify126.0ms

prune366.0ms

localize18.0ms

rewrite13.0ms

series618.0ms

simplify47.0ms

prune351.0ms

regimes303.0ms

bsearch57.0ms

simplify1.0ms

end0.0ms

sample2.8s

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