Details

sample101.0ms

Algorithm

intervals

Results

38.0ms	724×	body	80	nan
10.0ms	186×	body	80	valid
8.0ms	26×	body	640	valid
7.0ms	9×	body	1280	valid
5.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify71.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

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))
6.1b	(log (- 1.0 y))

rewrite22.0ms

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:

17.0ms	(* (- z 1.0) (log (- 1.0 y)))
0.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
3.0ms	(log (- 1.0 y))

series276.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (- z 1.0) (log (- 1.0 y)))
192.0ms	(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

prune225.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

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

rewrite107.0ms

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:

23.0ms	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
43.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
28.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms	(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))

series467.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
63.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
49.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
212.0ms	(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))

simplify64.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1053	3803
1	5001	2532

prune883.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (- 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)))

0.1b

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
71×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
37×	`add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv`

Counts

3 → 132

Calls

3 calls:

0.0ms

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

28.0ms

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

0.0ms

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

series330.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms

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

52.0ms

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

174.0ms

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

simplify61.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	634	1102
1	3061	865
2	5002	862

prune502.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

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))
7.2b	(* z (pow y 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(* 0.5 (* z (pow y 2)))
0.0ms	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
0.0ms	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
6.0ms	(* z (pow y 2))

series201.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 0.5 (* z (pow y 2)))
36.0ms	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
99.0ms	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
31.0ms	(* z (pow y 2))

simplify183.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	232	531
1	850	455
2	4835	453
3	5001	453

prune249.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes191.0ms

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	24	14
1	24	14

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	24009×	body	80	nan
322.0ms	5885×	body	80	valid
248.0ms	803×	body	640	valid
144.0ms	238×	body	1280	valid
126.0ms	677×	body	320	valid
50.0ms	432×	body	160	valid