Details

sample125.0ms

Algorithm

intervals

Results

48.0ms	800×	body	80	nan
12.0ms	170×	body	80	valid
9.0ms	13×	body	1280	valid
8.0ms	23×	body	640	valid
7.0ms	34×	body	320	valid
5.0ms	17×	body	160	valid

simplify132.0ms

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: 7.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.2b	(* (- x 1.0) (log y))
6.3b	(log (- 1.0 y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-*l/`
11×	`pow1`
10×	`associate-+r+` `associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
7×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
6×	`associate-+l+` `add-log-exp`
4×	`frac-add`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 109

Calls

4 calls:

12.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
9.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series265.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
40.0ms	(* (- z 1.0) (log (- 1.0 y)))
57.0ms	(* (- x 1.0) (log y))
45.0ms	(log (- 1.0 y))

simplify68.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	621	970
1	2460	896
2	5003	883

prune336.0ms

Filtered

121 candidates to 91 candidates (75.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Merged error: 0.1b

Counts

122 → 6

localize24.0ms

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))

rewrite63.0ms

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:

20.0ms	(* 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))

series326.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
148.0ms	(+ (* (- x 1.0) (log y)) (* (- 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))))))
58.0ms	(* (- x 1.0) (log y))

simplify58.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune829.0ms

Filtered

235 candidates to 163 candidates (69.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	232	9	241

Merged error: 0.1b

Counts

241 → 9

localize23.0ms

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)))

rewrite59.0ms

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:

18.0ms	(+ (* (- 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))))))))
12.0ms	(* (- 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)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(+ (* (- 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))))))))
69.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
68.0ms	(* (log (sqrt y)) (- x 1.0))
56.0ms	(* (- x 1.0) (log (sqrt y)))

simplify80.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1645	5157
1	5003	5071

prune1.0s

Filtered

180 candidates to 135 candidates (75.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	180	9	189

Merged error: 0.1b

Counts

189 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite13.0ms

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)

series696.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (cbrt y) (cbrt y))
170.0ms	(cbrt y)
166.0ms	(cbrt y)
169.0ms	(cbrt y)

simplify88.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

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

prune465.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 0.1b

Counts

94 → 9

regimes313.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	43	30

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	24235×	body	80	nan
388.0ms	5788×	body	80	valid
273.0ms	768×	body	640	valid
203.0ms	307×	body	1280	valid
160.0ms	719×	body	320	valid
67.0ms	458×	body	160	valid