Details

sample96.0ms

Algorithm

intervals

Results

34.0ms	701×	body	80	nan
11.0ms	198×	body	80	valid
8.0ms	25×	body	640	valid
6.0ms	9×	body	1280	valid
4.0ms	19×	body	320	valid
1.0ms	5×	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: 4.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.2b	(* (- x 1.0) (log y))
5.2b	(log (- 1.0 y))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

31.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
9.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series317.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
42.0ms	(* (- z 1.0) (log (- 1.0 y)))
61.0ms	(* (- x 1.0) (log y))
48.0ms	(log (- 1.0 y))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	539	1004
1	1900	915
2	5001	902

prune380.0ms

Filtered

132 candidates to 91 candidates (68.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	6	133

Merged error: 0.1b

Counts

133 → 6

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)))))))
0.2b	(* (- x 1.0) (log y))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
86×	`associate-r`
80×	`times-frac`
62×	`unpow-prod-down`
54×	`add-cube-cbrt`
33×	`associate-l`
31×	`add-exp-log`
27×	`flip3--` `flip--`
26×	`unpow2` `sqr-pow`
25×	`associate-*r/`
24×	`log-prod` `associate-*l/`
19×	`unswap-sqr`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
16×	`pow1` `distribute-rgt-in` `distribute-lft-in` `frac-add`
13×	`add-cbrt-cube`
12×	`frac-times` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp` `associate-/l*`
8×	`associate-/r*`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `log-pow` `add-log-exp`
4×	`sub-neg` `cbrt-unprod`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`clear-num` `un-div-inv`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 260

Calls

4 calls:

24.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
72.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
96.0ms	(+ (* (- 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))

series336.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
71.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
158.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
57.0ms	(* (- x 1.0) (log y))

simplify65.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1371	3003
1	5001	2848

prune1.1s

Filtered

272 candidates to 178 candidates (65.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	267	5	272
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	271	7	278

Merged error: 0.1b

Counts

278 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
0.2b	(cbrt (- z 1.0))
0.2b	(cbrt (- z 1.0))
0.2b	(cbrt (- z 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 104

Calls

4 calls:

15.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
3.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))

series443.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
102.0ms	(cbrt (- z 1.0))
105.0ms	(cbrt (- z 1.0))
104.0ms	(cbrt (- z 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	377	875
1	1271	824
2	5001	755

prune600.0ms

Filtered

116 candidates to 79 candidates (68.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Merged error: 0.1b

Counts

123 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* z (pow y 2)))
0.0b	(- (* 0.5 (pow y 2)) (+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2)))))
0.2b	(* (- x 1.0) (log y))
7.7b	(* z (pow y 2))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`associate-r`
27×	`associate-l`
22×	`unswap-sqr`
21×	`add-exp-log`
16×	`add-cube-cbrt`
14×	`pow1`
13×	`add-cbrt-cube`
11×	`prod-exp` `distribute-lft-out--`
10×	`unpow-prod-down`
9×	`add-log-exp`
8×	`distribute-lft-out`
6×	`log-prod` `unpow2` `difference-of-squares` `sqr-pow`
5×	`pow-prod-down` `cbrt-unprod`
4×	`*-commutative`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`pow-to-exp` `flip3--` `diff-log` `associate-*l/` `pow-exp` `flip--` `associate--r+`
1×	`+-commutative` `sub-neg` `sum-log` `log-pow`

Counts

4 → 131

Calls

4 calls:

14.0ms	(* 0.5 (* z (pow y 2)))
54.0ms	(- (* 0.5 (pow y 2)) (+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2)))))
10.0ms	(* (- x 1.0) (log y))
7.0ms	(* z (pow y 2))

series164.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* 0.5 (* z (pow y 2)))
38.0ms	(- (* 0.5 (pow y 2)) (+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2)))))
63.0ms	(* (- x 1.0) (log y))
31.0ms	(* z (pow y 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	507	930
1	2043	812
2	5001	802

prune398.0ms

Filtered

143 candidates to 85 candidates (59.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	144	6	150

Merged error: 0.1b

Counts

150 → 6

regimes284.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	21
1	32	21

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	23670×	body	80	nan
320.0ms	5890×	body	80	valid
239.0ms	770×	body	640	valid
163.0ms	264×	body	1280	valid
127.0ms	672×	body	320	valid
50.0ms	435×	body	160	valid