Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify139.0ms

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: 23.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
1.2b	(+ (* x y) (* z (- t a)))
23.0b	(/ (+ (* 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))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* z (- b y))
38.0ms	(* z (- t a))
50.0ms	(+ (* x y) (* z (- t a)))
353.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify91.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (75.0ms)

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

prune503.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (+ y (* z (- b y))))
1.2b	(+ (* x y) (* z (- t a)))
22.9b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite52.0ms

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:

12.0ms	(* z (- t a))
4.0ms	(/ 1 (+ y (* z (- b y))))
6.0ms	(+ (* x y) (* z (- t a)))
20.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* z (- t a))
93.0ms	(/ 1 (+ y (* z (- b y))))
49.0ms	(+ (* x y) (* z (- t a)))
354.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (75.0ms)

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

prune530.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.2b	(+ (* x y) (* z (- t a)))
23.0b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite54.0ms

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

series1.4s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* z (- t a))
1.0s	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
50.0ms	(+ (* x y) (* z (- t a)))
310.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify118.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (87.0ms)

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

prune633.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma (- b y) z y))
1.0b	(/ 1 (+ (* x y) (* z (- t a))))
1.2b	(+ (* x y) (* z (- t a)))
21.9b	(/ (/ 1 (fma (- b y) z y)) (/ 1 (+ (* x y) (* z (- t a)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

483×	`times-frac`
242×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
36×	`div-exp`
33×	`div-inv`
31×	`associate-/r/`
22×	`associate-+r+`
21×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-/l*`
18×	`prod-diff`
16×	`flip3-+` `flip-+`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`sub-neg` `pow-flip` `inv-pow`
1×	`+-commutative` `fma-def` `sum-log` `associate-/l/`

Counts

4 → 361

Calls

4 calls:

2.0ms	(/ 1 (fma (- b y) z y))
5.0ms	(/ 1 (+ (* x y) (* z (- t a))))
6.0ms	(+ (* x y) (* z (- t a)))
16.0ms	(/ (/ 1 (fma (- b y) z y)) (/ 1 (+ (* x y) (* z (- t a)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ 1 (fma (- b y) z y))
76.0ms	(/ 1 (+ (* x y) (* z (- t a))))
52.0ms	(+ (* x y) (* z (- t a)))
1.4s	(/ (/ 1 (fma (- b y) z y)) (/ 1 (+ (* x y) (* z (- t a)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1516	5862
1	5001	5259

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.7b

regimes442.0ms

Accuracy

32% (8.7b remaining)

Error of 19.7b against oracle of 11.0b and baseline of 23.8b

bsearch143.0ms

Steps

Iters	Range		Point
9	6.282190708703998e+62	1.435817206101045e+69	9.06086953674542e+67
10	-8.975163005195737e+106	-3.0124032878399176e+91	-3.0137375986476608e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	12
1	33	12

end0.0ms

sample672.0ms

Algorithm

intervals

Results

376.0ms

8399×

body

valid