Details

sample100.0ms

Algorithm

intervals

Results

37.0ms	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

simplify66.0ms

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: 4.9b

Counts

2 → 1

localize12.0ms

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))
5.2b	(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))

series292.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
204.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
45.0ms	(log (- 1.0 y))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

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

prune240.0ms

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))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

157×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
82×	`associate-r`
80×	`times-frac`
67×	`add-cube-cbrt`
62×	`unpow-prod-down`
56×	`prod-diff`
48×	`associate-l`
40×	`distribute-lft-out`
33×	`distribute-rgt-in` `distribute-lft-in`
28×	`add-exp-log`
26×	`pow1` `unpow2` `sqr-pow`
21×	`associate-*r/`
19×	`log-pow`
18×	`unswap-sqr`
11×	`prod-exp` `distribute-lft-out--`
10×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
8×	`associate-/r*`
6×	`pow-to-exp` `log-prod` `flip3--` `pow-exp` `associate--l+` `flip--`
4×	`frac-times`
3×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `-commutative` `difference-of-squares`
1×	`cbrt-undiv` `frac-2neg` `fma-udef` `div-inv`

Counts

3 → 249

Calls

3 calls:

27.0ms

(* 1/2 (/ (pow y 2) (pow 1.0 2)))

73.0ms

(* (- 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))

series339.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms

(* 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))

simplify123.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	972	3707
1	4520	2607
2	5001	2607

prune744.0ms

Filtered

258 candidates to 129 candidates (50.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	253	5	258
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	257	6	263

Merged error: 0.1b

Counts

263 → 6

localize22.0ms

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))

rewrite24.0ms

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×	`expm1-log1p-u` `frac-times` `cbrt-unprod` `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`

Counts

4 → 112

Calls

4 calls:

10.0ms	(* (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))

series424.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
98.0ms	(cbrt (- z 1.0))
104.0ms	(cbrt (- z 1.0))
98.0ms	(cbrt (- z 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	393	898
1	1351	849
2	5002	766

prune634.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0.1b

Counts

130 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* z (pow y 2)))
0.0b	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
0.1b	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
7.7b	(* z (pow y 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `associate-r`
19×	`add-exp-log`
17×	`unswap-sqr`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-cbrt-cube`
10×	`prod-exp`
9×	`unpow-prod-down` `associate-l`
5×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `pow-exp` `fma-udef`

Counts

4 → 96

Calls

4 calls:

12.0ms	(* 0.5 (* z (pow y 2)))
1.0ms	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
1.0ms	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
7.0ms	(* z (pow y 2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 0.5 (* z (pow y 2)))
37.0ms	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
105.0ms	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
33.0ms	(* z (pow y 2))

simplify44.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	298	663
1	1292	561
2	5001	557

prune363.0ms

Filtered

108 candidates to 73 candidates (67.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	108	6	114

Merged error: 0.1b

Counts

114 → 6

regimes256.0ms

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	21	12
1	21	12

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	23670×	body	80	nan
332.0ms	5890×	body	80	valid
239.0ms	770×	body	640	valid
164.0ms	264×	body	1280	valid
127.0ms	672×	body	320	valid
51.0ms	435×	body	160	valid