Details

sample103.0ms

Algorithm

intervals

Results

41.0ms	844×	body	80	nan
10.0ms	194×	body	80	valid
8.0ms	27×	body	640	valid
5.0ms	7×	body	1280	valid
3.0ms	17×	body	320	valid
1.0ms	13×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 6.7b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.7b	(log (- 1.0 y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `add-cbrt-cube`
4×	`associate-r` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3--` `associate-*l/` `log-pow` `flip--`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series290.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
206.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
41.0ms	(log (- 1.0 y))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449

prune237.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.1b

Counts

73 → 5

localize19.0ms

Local error

Found 3 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))))))

0.1b

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
60×	`*-un-lft-identity`
56×	`unpow-prod-down`
55×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`prod-diff` `unpow2` `sqr-pow`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
11×	`prod-exp`
10×	`add-cbrt-cube`
9×	`div-exp`
8×	`associate-l`
7×	`log-pow`
6×	`pow-to-exp` `log-prod` `flip3--` `pow-exp` `associate--l+` `flip--`
4×	`frac-times`
3×	`expm1-log1p-u` `associate-*r/` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `associate-l/` `-commutative` `difference-of-squares`
1×	`cbrt-undiv` `fma-udef` `div-inv`

Counts

3 → 189

Calls

3 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))))))

1.0ms

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

series333.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms

(* 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))))))

219.0ms

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

simplify117.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	933	2642
1	4282	1844
2	5001	1841

prune655.0ms

Filtered

198 candidates to 115 candidates (58.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	196	7	203

Merged error: 0.1b

Counts

203 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.6b	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.6b	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.6b	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

168×	`cbrt-div`
148×	`frac-times`
126×	`flip3--` `flip--`
50×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 170

Calls

4 calls:

11.0ms	(* (cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
9.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
9.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
9.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

423.0ms	(* (cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
246.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
246.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
242.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	647	7166
1	2098	6995
2	5001	6888

prune1.2s

Filtered

182 candidates to 132 candidates (72.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Merged error: 0.1b

Counts

189 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-prod`
52×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
22×	`pow1` `distribute-lft-out--`
18×	`cbrt-div`
15×	`add-cube-cbrt` `swap-sqr`
11×	`log-pow`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `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` `cbrt-unprod`

Counts

4 → 119

Calls

4 calls:

19.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
223.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
228.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
220.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	530	2983
1	1979	2840
2	5002	2543

prune633.0ms

Filtered

131 candidates to 92 candidates (70.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	131	7	138

Merged error: 0.1b

Counts

138 → 7

regimes252.0ms

Accuracy

0% (0.3b 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	25	14
1	25	14

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	24041×	body	80	nan
307.0ms	5857×	body	80	valid
237.0ms	789×	body	640	valid
146.0ms	244×	body	1280	valid
129.0ms	720×	body	320	valid
46.0ms	419×	body	160	valid