Details

sample100.0ms

Algorithm

intervals

Results

36.0ms	60×	body	1280	valid
12.0ms	38×	body	640	valid
8.0ms	116×	body	80	valid
5.0ms	25×	body	320	valid
4.0ms	4×	body	2560	valid
4.0ms	79×	body	80	nan
2.0ms	36×	body	80	overflowed
2.0ms	13×	body	160	valid
1.0ms	5×	body	640	nan
1.0ms	3×	body	1280	nan
1.0ms	6×	body	320	nan
0.0ms	3×	body	160	nan

simplify211.0ms

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: 25.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.4b	(+ (- 1.0 y) (* y (exp z)))
2.7b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite28.0ms

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)
9.0ms	(+ (- 1.0 y) (* y (exp z)))
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* y (exp z))
38.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
7.0ms	(+ (- 1.0 y) (* y (exp z)))
14.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

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

prune198.0ms

Filtered

68 candidates to 92 candidates (-35.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 5.8b

Counts

93 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow z 2))
0.0b	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
4.5b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
6.6b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log`
11×	`associate-r`
10×	`times-frac` `add-cbrt-cube`
6×	`pow1` `associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unpow2` `difference-of-squares` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 93

Calls

4 calls:

5.0ms	(* 0.5 (pow z 2))
8.0ms	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series71.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow z 2))
30.0ms	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
16.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
22.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify59.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	460	952
1	1914	882
2	5001	882

prune252.0ms

Filtered

73 candidates to 105 candidates (-43.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	9	105
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	97	14	111

Merged error: 5.7b

Counts

111 → 14

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
5.2b	(/ (* z y) t)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt`
3×	`times-frac` `associate-/r*`
2×	`pow1` `cbrt-undiv` `diff-log` `div-exp`
1×	`sub-neg` `flip3--` `frac-2neg` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 37

Calls

2 calls:

10.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.0ms	(/ (* z y) t)

series22.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
5.0ms	(/ (* z y) t)

simplify90.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	204	286
1	812	256
2	3760	256
3	5001	256

prune124.0ms

Filtered

29 candidates to 43 candidates (-48.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	34	9	43
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	41	16	57

Merged error: 4.8b

Counts

57 → 16

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (* (* z y) (/ 1 t))) (/ (log 1.0) t)))
5.3b	(* (* z y) (/ 1 t))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`associate-r`
12×	`prod-exp`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `times-frac`
7×	`pow1` `add-log-exp`
6×	`cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `rec-exp` `diff-log` `1-exp`
1×	`sub-neg` `flip3--` `associate-r/` `associate-l` `sum-log` `un-div-inv` `-commutative` `flip--` `div-inv` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 54

Calls

2 calls:

12.0ms	(- x (+ (* 1.0 (* (* z y) (/ 1 t))) (/ (log 1.0) t)))
9.0ms	(* (* z y) (/ 1 t))

series21.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- x (+ (* 1.0 (* (* z y) (/ 1 t))) (/ (log 1.0) t)))
5.0ms	(* (* z y) (/ 1 t))

simplify41.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	349	404
1	1639	338
2	5002	325

prune65.0ms

Filtered

35 candidates to 60 candidates (-71.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	61	15	76

Merged error: 4.8b

Counts

76 → 15

regimes1.0s

Accuracy

60.7% (5.3b remaining)

Error of 9.4b against oracle of 4.2b and baseline of 17.6b

bsearch91.0ms

Steps

Iters	Range		Point
7	-4.2844349760101216e-159	-2.1114174854462004e-161	-4.621734365912303e-161
6	-3.831560156749637e-05	-7.527464205469873e-06	-7.595480438183484e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	24
1	50	24

end0.0ms

sample2.9s

Algorithm

intervals

Results

860.0ms	1490×	body	1280	valid
532.0ms	1577×	body	640	valid
246.0ms	3510×	body	80	valid
185.0ms	857×	body	320	valid
111.0ms	2404×	body	80	nan
100.0ms	74×	body	2560	valid
79.0ms	1506×	body	80	overflowed
68.0ms	516×	body	160	valid
65.0ms	270×	body	640	nan
38.0ms	112×	body	1280	nan
34.0ms	192×	body	320	nan
11.0ms	110×	body	160	nan

Details

sample100.0ms

simplify211.0ms

prune4.0ms

localize10.0ms

rewrite28.0ms

series64.0ms

simplify48.0ms

prune198.0ms

localize13.0ms

rewrite28.0ms

series71.0ms

simplify59.0ms

prune252.0ms

localize9.0ms

rewrite15.0ms

series22.0ms

simplify90.0ms

prune124.0ms

localize10.0ms

rewrite23.0ms

series21.0ms

simplify41.0ms

prune65.0ms

regimes1.0s

bsearch91.0ms

simplify2.0ms

end0.0ms

sample2.9s

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