Details

sample109.0ms

Algorithm

intervals

Results

43.0ms	678×	body	80	nan
13.0ms	192×	body	80	valid
10.0ms	27×	body	640	valid
5.0ms	23×	body	320	valid
5.0ms	7×	body	1280	valid
1.0ms	9×	body	160	valid

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	49	9
2	118	9
3	256	9
4	533	9
5	1250	9
6	2637	9
7	4297	9
8	4573	9
9	4588	9
10	4588	9

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: 7.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.2b	(* (- x 1.0) (log y))
5.7b	(log (- 1.0 y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`log-prod`
13×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`flip3--` `associate-*l/` `flip--`
3×	`log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 94

Calls

4 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series303.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (- z 1.0) (log (- 1.0 y)))
154.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
59.0ms	(* (- x 1.0) (log y))
43.0ms	(log (- 1.0 y))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	498	803
1	1805	714
2	5001	701

prune281.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 0.0b

Counts

107 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b	(* (- x 1.0) (log y))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
57×	`*-un-lft-identity`
56×	`unpow-prod-down`
50×	`add-cube-cbrt`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`distribute-rgt-in` `distribute-lft-in` `frac-add`
13×	`associate-l` `add-cbrt-cube`
12×	`pow1` `frac-times` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`sub-neg` `cbrt-unprod` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`log-pow`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 223

Calls

4 calls:

23.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (- x 1.0) (log y))

series325.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
151.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
56.0ms	(* (- x 1.0) (log y))

simplify63.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune806.0ms

Filtered

235 candidates to 163 candidates (69.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	235	8	243

Merged error: 0.0b

Counts

243 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log (sqrt y))) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b	(* (log (sqrt y)) (- x 1.0))
0.2b	(* (- x 1.0) (log (sqrt y)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

68×	`frac-add`
66×	`flip3--` `flip--`
48×	`associate-*l/`
44×	`associate-*r/`
34×	`add-sqr-sqrt`
30×	`log-prod`
29×	`*-un-lft-identity`
20×	`frac-times` `add-cube-cbrt`
19×	`distribute-rgt-in` `distribute-lft-in`
17×	`associate-r`
16×	`associate-l`
15×	`pow1`
12×	`associate-+l+` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-log-exp`
7×	`log-pow`
6×	`associate--l+`
5×	`distribute-lft-out--`
4×	`sub-neg` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2`
1×	`+-commutative` `associate-+r+`

Counts

4 → 168

Calls

4 calls:

20.0ms	(+ (* (- x 1.0) (log (sqrt y))) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
13.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (log (sqrt y)) (- x 1.0))
8.0ms	(* (- x 1.0) (log (sqrt y)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(+ (* (- x 1.0) (log (sqrt y))) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
66.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
69.0ms	(* (log (sqrt y)) (- x 1.0))
58.0ms	(* (- x 1.0) (log (sqrt y)))

simplify88.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1645	5157
1	5003	5071

prune914.0ms

Filtered

180 candidates to 135 candidates (75.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	179	9	188

Merged error: 0.0b

Counts

188 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series760.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (cbrt y) (cbrt y))
210.0ms	(cbrt y)
180.0ms	(cbrt y)
182.0ms	(cbrt y)

simplify86.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune345.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

regimes361.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	21
1	33	21
2	33	21

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	23952×	body	80	nan
394.0ms	5795×	body	80	valid
282.0ms	792×	body	640	valid
187.0ms	273×	body	1280	valid
166.0ms	737×	body	320	valid
60.0ms	432×	body	160	valid

Details

sample109.0ms

simplify137.0ms

prune3.0ms

localize13.0ms

rewrite35.0ms

series303.0ms

simplify49.0ms

prune281.0ms

localize21.0ms

rewrite64.0ms

series325.0ms

simplify63.0ms

prune806.0ms

localize24.0ms

rewrite58.0ms

series384.0ms

simplify88.0ms

prune914.0ms

localize27.0ms

rewrite11.0ms

series760.0ms

simplify86.0ms

prune345.0ms

regimes361.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.5s

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