Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify143.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 23.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
1.1b	(+ (* x y) (* z (- t a)))
22.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

16.0ms	(* z (- b y))
12.0ms	(* z (- t a))
6.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* z (- b y))
38.0ms	(* z (- t a))
50.0ms	(+ (* x y) (* z (- t a)))
359.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify90.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune490.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.1b	(+ (* x y) (* z (- t a)))
22.6b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

12.0ms	(* z (- t a))
11.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
7.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* z (- t a))
901.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
45.0ms	(+ (* x y) (* z (- t a)))
295.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify105.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	716	2474
1	3125	2063
2	5002	1958

prune600.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.8b	(fma x y (* z (- t a)))
0.9b	(/ 1 (fma (- b y) z y))
22.3b	(* (/ 1 (fma (- b y) z y)) (fma x y (* z (- t a))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-l`
13×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `cbrt-unprod` `fma-udef` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `div-inv`
1×	`flip3--` `pow-flip` `frac-2neg` `associate-*l/` `clear-num` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 128

Calls

4 calls:

12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
3.0ms	(/ 1 (fma (- b y) z y))
9.0ms	(* (/ 1 (fma (- b y) z y)) (fma x y (* z (- t a))))

series1.6s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* z (- t a))
57.0ms	(fma x y (* z (- t a)))
113.0ms	(/ 1 (fma (- b y) z y))
1.3s	(* (/ 1 (fma (- b y) z y)) (fma x y (* z (- t a))))

simplify73.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	413	990
1	1644	767
2	5001	741

prune417.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (- t a))
0.8b	(fma x y (* z (- t a)))
22.6b	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-r`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`sub-neg` `associate-*r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 85

Calls

3 calls:

12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

series477.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* z (- t a))
52.0ms	(fma x y (* z (- t a)))
380.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

simplify160.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	291	724
1	1049	551
2	4904	521
3	5001	521

prune241.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.6b

regimes468.0ms

Accuracy

3.9% (11.8b remaining)

Error of 22.7b against oracle of 10.9b and baseline of 23.1b

bsearch56.0ms

Steps

Iters	Range		Point
9	8.00038015319445e+168	2.754241618685784e+175	3.523447744044644e+170

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	16	6

end0.0ms

sample653.0ms

Algorithm

intervals

Results

365.0ms

8413×

body

valid