Details

sample99.0ms

Algorithm

intervals

Results

36.0ms	818×	body	80	nan
9.0ms	31×	body	640	valid
8.0ms	14×	body	1280	valid
8.0ms	175×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 10.4b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (log y)) (* z (log (- 1.0 y))))
0.0b	(* z (log (- 1.0 y)))
0.2b	(* x (log y))
7.8b	(log (- 1.0 y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`associate-+r+`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`associate-+l+` `associate-l` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `fma-def` `flip3-+` `rem-log-exp` `sum-log` `flip--` `flip-+`

Counts

4 → 106

Calls

4 calls:

7.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
6.0ms	(* z (log (- 1.0 y)))
4.0ms	(* x (log y))
4.0ms	(log (- 1.0 y))

series218.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
65.0ms	(* z (log (- 1.0 y)))
41.0ms	(* x (log y))
41.0ms	(log (- 1.0 y))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	496	683
1	1771	625
2	5001	600

prune458.0ms

Filtered

118 candidates to 85 candidates (72.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	7	120

Merged error: 0.0b

Counts

120 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
80×	`times-frac`
78×	`add-cube-cbrt` `associate-r`
56×	`unpow-prod-down`
48×	`prod-diff`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
31×	`add-exp-log`
24×	`pow1` `log-prod` `unpow2` `sqr-pow`
19×	`unswap-sqr`
14×	`log-pow`
13×	`add-cbrt-cube`
12×	`prod-exp` `associate--l+`
9×	`div-exp` `associate-l`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-r/` `pow-prod-down` `-commutative`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `flip3--` `fma-def` `flip3-+` `sum-log` `flip--` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 252

Calls

4 calls:

20.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
10.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* x (log y))

series313.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
128.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
101.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
36.0ms	(* x (log y))

simplify124.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1032	3139
1	4195	2176
2	5001	2168

prune703.0ms

Filtered

264 candidates to 156 candidates (59.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	263	8	271

Merged error: 0.0b

Counts

271 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`log-prod` `prod-diff`
23×	`distribute-rgt-in` `distribute-lft-in`
19×	`pow1`
13×	`log-pow`
12×	`associate-r`
9×	`add-exp-log` `sqrt-prod`
8×	`add-cbrt-cube`
6×	`associate-l` `associate--l+`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`flip3--` `rem-log-exp` `flip--` `fma-udef` `difference-of-squares`

Counts

4 → 123

Calls

4 calls:

2.0ms	(log (sqrt y))
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms	(* x (log (sqrt y)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(log (sqrt y))
98.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
160.0ms	(fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
119.0ms	(* x (log (sqrt y)))

simplify65.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	489	2024
1	1887	1315
2	5001	1269

prune410.0ms

Filtered

135 candidates to 76 candidates (56.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 0.0b

Counts

143 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (log (sqrt y)))
0.3b	(+ (* 2 (log (cbrt (sqrt y)))) (log (cbrt (sqrt y))))
0.7b	(cbrt (sqrt y))
0.7b	(cbrt (sqrt y))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod`
30×	`cbrt-prod`
25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`sqrt-prod`
18×	`associate-+l+`
15×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1` `associate-+r+`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`associate-l`
2×	`distribute-rgt-out` `pow1/3`
1×	`+-commutative` `fma-def` `distribute-lft1-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

5.0ms	(* x (log (sqrt y)))
9.0ms	(+ (* 2 (log (cbrt (sqrt y)))) (log (cbrt (sqrt y))))
2.0ms	(cbrt (sqrt y))
2.0ms	(cbrt (sqrt y))

series618.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* x (log (sqrt y)))
229.0ms	(+ (* 2 (log (cbrt (sqrt y)))) (log (cbrt (sqrt y))))
153.0ms	(cbrt (sqrt y))
149.0ms	(cbrt (sqrt y))

simplify44.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	413	782
1	1276	702
2	5001	659

prune575.0ms

Filtered

123 candidates to 95 candidates (77.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	123	8	131

Merged error: 0.0b

Counts

131 → 8

regimes175.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	23888×	body	80	nan
271.0ms	5588×	body	80	valid
243.0ms	846×	body	640	valid
237.0ms	404×	body	1280	valid
121.0ms	720×	body	320	valid
49.0ms	478×	body	160	valid