Details

sample102.0ms

Algorithm

intervals

Results

36.0ms	839×	body	80	nan
8.0ms	176×	body	80	valid
8.0ms	30×	body	640	valid
7.0ms	12×	body	1280	valid
5.0ms	14×	body	160	valid
4.0ms	24×	body	320	valid

simplify29.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.2b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
5.2b	(log (- 1.0 y))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

6.0ms	(* z (log (- 1.0 y)))
1.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series229.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* z (log (- 1.0 y)))
115.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
45.0ms	(log (- 1.0 y))

simplify103.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366

prune212.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 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))))))
0.1b	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
58×	`*-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`
7×	`log-pow`
6×	`pow-to-exp` `log-prod` `associate-l` `pow-exp` `associate--l+`
3×	`expm1-log1p-u` `associate-*r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `*-commutative` `distribute-lft-out--`
1×	`cbrt-undiv` `flip3--` `flip--` `fma-udef` `div-inv` `difference-of-squares`

Counts

3 → 181

Calls

3 calls:

23.0ms	(* 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))))))
1.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series317.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
100.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
163.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify94.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	809	2340
1	3464	1552
2	5001	1546

prune563.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.6b	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.6b	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.6b	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (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:

1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
5.0ms	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

series1.3s

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
323.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
323.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
344.0ms	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

simplify59.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	421	2516
1	1546	2319
2	5002	2069

prune477.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-prod`
24×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`pow1` `*-un-lft-identity`
12×	`associate-r`
11×	`add-exp-log` `pow1/3`
7×	`swap-sqr` `associate-l` `pow-prod-down`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
8.0ms	(* (* (cbrt (* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))) (cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
6.0ms	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

series1.3s

Counts

4 → 12

Calls

4 calls:

319.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
318.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
357.0ms	(* (* (cbrt (* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))) (cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
348.0ms	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	497	3900
1	1975	3521
2	5001	3188

prune584.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

regimes274.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	24011×	body	80	nan
271.0ms	5595×	body	80	valid
262.0ms	935×	body	640	valid
218.0ms	378×	body	1280	valid
116.0ms	682×	body	320	valid
48.0ms	438×	body	160	valid