Details

sample110.0ms

Algorithm

intervals

Results

41.0ms	672×	body	80	nan
12.0ms	185×	body	80	valid
10.0ms	29×	body	640	valid
8.0ms	21×	body	320	valid
6.0ms	9×	body	1280	valid
2.0ms	13×	body	160	valid

simplify125.0ms

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: 5.9b

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)))) t)
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(* (- x 1.0) (log y))
4.5b	(log (- 1.0 y))

rewrite31.0ms

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:

10.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
8.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series301.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
46.0ms	(* (- z 1.0) (log (- 1.0 y)))
53.0ms	(* (- x 1.0) (log y))
45.0ms	(log (- 1.0 y))

simplify50.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

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

prune289.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	7	107

Merged error: 0.1b

Counts

107 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

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

series523.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
149.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
67.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
59.0ms	(* (- x 1.0) (log y))

simplify124.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	888	2535
1	4674	2460
2	5001	2448

prune702.0ms

Filtered

141 candidates to 107 candidates (75.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 0.1b

Counts

148 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.2b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
12×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`frac-add`
3×	`pow1/3`
2×	`log-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

8.0ms	(* (- x 1.0) (log (cbrt y)))
14.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series633.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- x 1.0) (log (cbrt y)))
163.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
170.0ms	(cbrt y)
172.0ms	(cbrt y)

simplify76.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	522	1002
1	2415	876
2	5003	829

prune613.0ms

Filtered

122 candidates to 103 candidates (84.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 0.1b

Counts

130 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (cbrt y)) (sqrt (cbrt y)))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`sqrt-prod`
27×	`cbrt-prod`
19×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
14×	`sqrt-pow1`
11×	`swap-sqr`
9×	`pow1/3` `associate-r` `associate-l` `unswap-sqr`
8×	`pow1/2`
6×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`pow-prod-down` `pow-sqr` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 99

Calls

4 calls:

9.0ms	(* (sqrt (cbrt y)) (sqrt (cbrt y)))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series715.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (sqrt (cbrt y)) (sqrt (cbrt y)))
175.0ms	(cbrt y)
181.0ms	(cbrt y)
179.0ms	(cbrt y)

simplify161.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	140	393
1	583	351
2	3616	326
3	5001	317

prune433.0ms

Filtered

111 candidates to 69 candidates (62.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Merged error: 0.1b

Counts

119 → 8

regimes292.0ms

Accuracy

0% (0.4b 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	38	26
1	38	26

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	23982×	body	80	nan
404.0ms	5858×	body	80	valid
267.0ms	751×	body	640	valid
189.0ms	274×	body	1280	valid
153.0ms	685×	body	320	valid
67.0ms	459×	body	160	valid