Details

sample125.0ms

Algorithm

intervals

Results

53.0ms	802×	body	80	nan
12.0ms	183×	body	80	valid
10.0ms	27×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	7×	body	1280	valid
2.0ms	15×	body	160	valid

simplify134.0ms

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: 7.1b

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)))
0.1b	(* (- x 1.0) (log y))
6.7b	(log (- 1.0 y))

rewrite33.0ms

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:

11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
8.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series271.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
47.0ms	(* (- z 1.0) (log (- 1.0 y)))
55.0ms	(* (- x 1.0) (log y))
47.0ms	(log (- 1.0 y))

simplify66.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (55.0ms)

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

prune346.0ms

Filtered

121 candidates to 91 candidates (75.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	8	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Merged error: 0.1b

Counts

122 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))))))
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(* (- x 1.0) (log y))

rewrite65.0ms

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:

19.0ms	(* 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))))))
15.0ms	(+ (* (- x 1.0) (log y)) (* (- 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))

series339.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 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))))))
152.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
61.0ms	(* (- 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

prune826.0ms

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: 0.1b

Counts

243 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt y))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(* (log (sqrt y)) (- x 1.0))
0.1b	(* (- x 1.0) (log (sqrt y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
24×	`log-prod`
18×	`add-cube-cbrt`
17×	`pow1` `associate-r`
16×	`associate-l`
13×	`distribute-rgt-in` `distribute-lft-in`
11×	`add-exp-log`
10×	`log-pow` `add-cbrt-cube`
9×	`sqrt-prod`
8×	`flip3--` `flip--`
6×	`associate--l+`
5×	`distribute-lft-out--`
4×	`frac-times` `sub-neg` `associate-r/` `associate-l/` `add-log-exp` `difference-of-squares`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp`

Counts

4 → 124

Calls

4 calls:

2.0ms	(log (sqrt y))
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))
11.0ms	(* (- x 1.0) (log (sqrt y)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(log (sqrt y))
72.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
67.0ms	(* (log (sqrt y)) (- x 1.0))
66.0ms	(* (- x 1.0) (log (sqrt y)))

simplify69.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	559	1223
1	2515	1120
2	5002	1102

prune505.0ms

Filtered

136 candidates to 89 candidates (65.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 0.0b

Counts

144 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(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:

5.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series755.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt y) (cbrt y))
192.0ms	(cbrt y)
180.0ms	(cbrt y)
181.0ms	(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

prune413.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 0.0b

Counts

93 → 7

regimes262.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	23982×	body	80	nan
393.0ms	5822×	body	80	valid
291.0ms	810×	body	640	valid
171.0ms	255×	body	1280	valid
165.0ms	734×	body	320	valid
60.0ms	425×	body	160	valid