Details

sample79.0ms

Algorithm

intervals

Results

18.0ms	32×	body	1280	valid
17.0ms	52×	body	640	valid
9.0ms	123×	body	80	valid
7.0ms	32×	body	320	valid
3.0ms	73×	body	80	nan
2.0ms	17×	body	160	valid
2.0ms	35×	body	80	overflowed
2.0ms	9×	body	320	nan
2.0ms	4×	body	1280	nan
1.0ms	4×	body	640	nan
1.0ms	1×	body	2560	valid
0.0ms	1×	body	160	nan

simplify210.0ms

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: 22.7b

Counts

2 → 1

localize11.0ms

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))))
3.0b	(+ (- 1.0 y) (* y (exp z)))

rewrite32.0ms

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))
11.0ms	(/ (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)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
152.0ms	(/ (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)))

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune308.0ms

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: 5.1b

Counts

115 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.9b	(log (+ 1.0 (* y (expm1 z))))

rewrite15.0ms

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

series261.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* y (expm1 z))
152.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
69.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify52.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (44.0ms)

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

prune225.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 5.1b

Counts

86 → 7

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
3.9b	(log (+ 1.0 (* y (expm1 z))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-exp-log` `*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`times-frac`
10×	`add-cbrt-cube`
9×	`pow1`
7×	`associate-l`
5×	`prod-exp`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `log-prod` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `div-exp` `pow-prod-down` `log-pow` `*-commutative`
1×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-*r/` `rem-log-exp` `un-div-inv` `flip-+` `div-inv`

Counts

3 → 75

Calls

3 calls:

4.0ms	(* y (expm1 z))
8.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series267.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* y (expm1 z))
151.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify62.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	517	632
1	2266	551
2	5002	519

prune225.0ms

Filtered

84 candidates to 64 candidates (76.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 5.1b

Counts

91 → 7

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (log (fma (expm1 z) y 1.0)) t)
3.9b	(log (fma (expm1 z) y 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`pow1`
5×	`add-exp-log` `log-pow`
4×	`add-cbrt-cube` `associate-/l*`
3×	`log-prod` `associate-/r*`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

2 → 47

Calls

2 calls:

4.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
2.0ms	(log (fma (expm1 z) y 1.0))

series195.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
64.0ms	(log (fma (expm1 z) y 1.0))

simplify132.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	275	405
1	928	372
2	4552	366
3	5001	365

prune137.0ms

Filtered

53 candidates to 41 candidates (77.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	53	7	60

Merged error: 5.1b

Counts

60 → 7

regimes249.0ms

Accuracy

41% (4.0b remaining)

Error of 8.6b against oracle of 4.6b and baseline of 11.4b

bsearch86.0ms

Steps

Iters	Range		Point
8	-1.2112078485307249e-60	-2.378790775115244e-63	-3.2314583272364048e-62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	23
1	27	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

845.0ms	1415×	body	1280	valid
535.0ms	1570×	body	640	valid
252.0ms	3523×	body	80	valid
212.0ms	956×	body	320	valid
121.0ms	2503×	body	80	nan
106.0ms	74×	body	2560	valid
85.0ms	1521×	body	80	overflowed
69.0ms	491×	body	160	valid
63.0ms	248×	body	640	nan
49.0ms	131×	body	1280	nan
33.0ms	193×	body	320	nan
13.0ms	123×	body	160	nan