Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

274×

body

valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- b y))
0.9b	(+ (* x y) (* z (- t a)))
20.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
44×	`associate-+r+`
33×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `sub-neg`
5×	`associate-r`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`+-commutative` `associate-*r/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

5.0ms	(+ y (* z (- b y)))
11.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ y (* z (- b y)))
34.0ms	(* z (- b y))
43.0ms	(+ (* x y) (* z (- t a)))
303.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify71.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	602	1288
1	2282	956
2	5001	937

prune448.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(/ 1 (+ y (* z (- b y))))
0.9b	(+ (* x y) (* z (- t a)))
20.8b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac` `associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `prod-exp` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

11.0ms	(* z (- b y))
4.0ms	(/ 1 (+ y (* z (- b y))))
6.0ms	(+ (* x y) (* z (- t a)))
18.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* z (- b y))
80.0ms	(/ 1 (+ y (* z (- b y))))
40.0ms	(+ (* x y) (* z (- t a)))
302.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	658	1375
1	2830	1048
2	5001	1011

prune429.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.3b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.8b	(fma x y (* z (- t a)))
20.8b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma z (- b y) y)
5.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series614.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma z (- b y) y)
450.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
48.0ms	(fma x y (* z (- t a)))
93.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify49.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	363	1470
1	1455	1364
2	5001	1292

prune396.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 9.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
0.6b	(cbrt b)
0.9b	(+ (* x y) (* z (- t a)))
20.9b	(/ (+ (* x y) (* z (- t a))) (+ (fma (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1))) z y) (* (fma (- y) 1 (* y 1)) z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`associate-+r+`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`sub-neg` `pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

0.0ms	(cbrt b)
0.0ms	(cbrt b)
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ (fma (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1))) z y) (* (fma (- y) 1 (* y 1)) z)))

series1.9s

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt b)
176.0ms	(cbrt b)
45.0ms	(+ (* x y) (* z (- t a)))
1.4s	(/ (+ (* x y) (* z (- t a))) (+ (fma (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1))) z y) (* (fma (- y) 1 (* y 1)) z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	1272
1	1430	1111
2	5001	1085

prune495.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.6b

regimes514.0ms

Accuracy

18.1% (18.2b remaining)

Error of 19.6b against oracle of 1.5b and baseline of 23.6b

bsearch132.0ms

Steps

Iters	Range	Point
8	1.2162973021129088e+287	8.047078378951813e+290	2.5216575634682354e+288
8	9.272978597534178e+111	9.10834597569885e+114	3.5521863173674646e+112
7	-1.8015446945155894e+92	-8.626610833871534e+89	-3.176738704950571e+91

Iters

Range

Point

1.2162973021129088e+287

8.047078378951813e+290

2.5216575634682354e+288

9.272978597534178e+111

9.10834597569885e+114

3.5521863173674646e+112

-1.8015446945155894e+92

-8.626610833871534e+89

-3.176738704950571e+91

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample628.0ms

Algorithm

intervals

Results

344.0ms

8448×

body

valid