Details

sample30.0ms

Algorithm

intervals

Results

13.0ms

266×

body

valid

simplify149.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
0.4b	(+ (* x y) (* z (- t a)))
23.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite105.0ms

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:

25.0ms	(* z (- b y))
22.0ms	(* z (- t a))
13.0ms	(+ (* x y) (* z (- t a)))
37.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* z (- b y))
41.0ms	(* z (- t a))
42.0ms	(+ (* x y) (* z (- t a)))
341.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify93.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (77.0ms)

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

prune860.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.4b	(+ (* x y) (* z (- t a)))
0.8b	(/ 1 (+ y (* z (- b y))))
23.4b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite98.0ms

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:

22.0ms	(* z (- t a))
13.0ms	(+ (* x y) (* z (- t a)))
10.0ms	(/ 1 (+ y (* z (- b y))))
44.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* z (- t a))
41.0ms	(+ (* x y) (* z (- t a)))
87.0ms	(/ 1 (+ y (* z (- b y))))
336.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	594	1375
1	2523	1048
2	5001	1011

prune868.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.4b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
0.4b	(+ (* x y) (* z (- t a)))
23.7b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite108.0ms

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:

26.0ms	(* z (- t a))
23.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
13.0ms	(+ (* x y) (* z (- t a)))
37.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.2s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* z (- t a))
859.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
42.0ms	(+ (* x y) (* z (- t a)))
281.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify101.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (77.0ms)

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

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b y))
0.5b	(cbrt (- b y))
0.6b	(* (cbrt (- b y)) (cbrt (- b y)))
23.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
38×	`cbrt-prod`
22×	`add-cube-cbrt`
16×	`cbrt-div`
11×	`pow1`
10×	`swap-sqr`
9×	`times-frac`
8×	`add-exp-log` `flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-cbrt-cube` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `pow-sqr` `pow-prod-up` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 125

Calls

4 calls:

4.0ms	(cbrt (- b y))
4.0ms	(cbrt (- b y))
40.0ms	(* (cbrt (- b y)) (cbrt (- b y)))
33.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- b y))
152.0ms	(cbrt (- b y))
138.0ms	(* (cbrt (- b y)) (cbrt (- b y)))
578.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	470	1448
1	1864	1341
2	5001	1261

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 23.8b

regimes773.0ms

Accuracy

0% (0.7b remaining)

Error of 23.5b against oracle of 22.8b and baseline of 23.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	24	9

end0.0ms

sample729.0ms

Algorithm

intervals

Results

423.0ms

8420×

body

valid