Details

sample111.0ms

Algorithm

intervals

Results

44.0ms	818×	body	80	nan
10.0ms	181×	body	80	valid
8.0ms	25×	body	640	valid
8.0ms	11×	body	1280	valid
5.0ms	28×	body	320	valid
2.0ms	14×	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

prune7.0ms

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: 8.8b

Counts

2 → 1

localize13.0ms

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))
7.8b	(log (- 1.0 y))

rewrite18.0ms

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))

series287.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (- z 1.0) (log (- 1.0 y)))
199.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
41.0ms	(log (- 1.0 y))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (29.0ms)

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

prune204.0ms

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

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
80×	`times-frac`
78×	`*-un-lft-identity`
74×	`associate-r`
73×	`add-cube-cbrt`
56×	`unpow-prod-down`
51×	`prod-diff`
46×	`associate--l+`
34×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
21×	`pow1`
18×	`unswap-sqr`
13×	`log-pow`
12×	`log-prod`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
8×	`associate-l`
7×	`flip3--` `flip--`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`associate-*r/` `cbrt-unprod` `distribute-lft-out--`
2×	`pow-prod-down` `associate-l/` `-commutative` `difference-of-squares`
1×	`cbrt-undiv` `fma-neg` `diff-log` `fma-udef` `div-inv`

Counts

4 → 241

Calls

4 calls:

15.0ms	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
20.0ms	(* 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))

series490.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
48.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
226.0ms	(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))

simplify130.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1053	3734
1	4672	2536
2	5001	2536

prune784.0ms

Filtered

253 candidates to 157 candidates (62.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	251	7	258

Merged error: 0.0b

Counts

258 → 7

localize24.0ms

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

rewrite35.0ms

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:

15.0ms	(* (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))))))

series951.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (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))))))
224.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
227.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (44.0ms)

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

prune595.0ms

Filtered

131 candidates to 92 candidates (70.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Merged error: 0.0b

Counts

138 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (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))) (cbrt (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))))
0.5b	(cbrt (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)))
0.5b	(cbrt (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)))
0.5b	(cbrt (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)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (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))) (cbrt (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))))
1.0ms	(cbrt (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)))
1.0ms	(cbrt (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)))
1.0ms	(cbrt (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)))

series1.8s

Counts

4 → 12

Calls

4 calls:

711.0ms	(* (cbrt (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))) (cbrt (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))))
372.0ms	(cbrt (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)))
374.0ms	(cbrt (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)))
367.0ms	(cbrt (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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	408	2733
1	1367	2487
2	5001	2281

prune438.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	92	8	100

Merged error: 0.0b

Counts

100 → 8

regimes299.0ms

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	25	14
1	25	14

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	23888×	body	80	nan
339.0ms	5906×	body	80	valid
234.0ms	745×	body	640	valid
171.0ms	272×	body	1280	valid
130.0ms	662×	body	320	valid
58.0ms	451×	body	160	valid