Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

270×

body

valid

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	8
1	37	8
2	65	8
3	94	8
4	108	8
5	132	8
6	201	8
7	359	8
8	825	8
9	3212	8
10	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
1.2b	(+ (* x y) (* z (- t a)))
22.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `add-log-exp`
4×	`associate-+r+` `associate-*r/`
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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 98

Calls

4 calls:

10.0ms	(* z (- t a))
13.0ms	(* z (- b y))
4.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* z (- t a))
50.0ms	(* z (- b y))
42.0ms	(+ (* x y) (* z (- t a)))
302.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	401	714
1	1759	659
2	5001	659

prune294.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(/ 1 (+ y (* z (- b y))))
1.2b	(+ (* x y) (* z (- t a)))
22.0b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
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×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `div-exp` `associate-/r/` `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` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

10.0ms	(* z (- b y))
4.0ms	(/ 1 (+ y (* z (- b y))))
3.0ms	(+ (* x y) (* z (- t a)))
19.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* z (- b y))
79.0ms	(/ 1 (+ y (* z (- b y))))
44.0ms	(+ (* x y) (* z (- t a)))
327.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	449	957
1	2234	849
2	5001	823

prune299.0ms

Filtered

128 candidates to 77 candidates (60.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.2b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.2b	(+ (* x y) (* z (- t a)))
22.3b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
62×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
58×	`add-cube-cbrt`
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` `distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in`
3×	`associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `associate-/l/`
1×	`+-commutative` `flip3--` `pow-flip` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

10.0ms	(* z (- b y))
10.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
3.0ms	(+ (* x y) (* z (- t a)))
13.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* z (- b y))
797.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
39.0ms	(+ (* x y) (* z (- t a)))
254.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify77.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	576	2059
1	2790	1881
2	5001	1793

prune381.0ms

Filtered

168 candidates to 95 candidates (56.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b y))
0.5b	(cbrt (- b y))
1.2b	(+ (* x y) (* z (- t a)))
22.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
10×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `cbrt-div` `associate-+r+`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow1/3` `associate-/r/` `flip--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 76

Calls

4 calls:

2.0ms	(cbrt (- b y))
2.0ms	(cbrt (- b y))
3.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- b y))
148.0ms	(cbrt (- b y))
47.0ms	(+ (* x y) (* z (- t a)))
308.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	380	1064
1	1283	970
2	5001	962

prune325.0ms

Filtered

88 candidates to 72 candidates (81.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.4b

regimes323.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	24	9
1	24	9

end0.0ms

sample685.0ms

Algorithm

intervals

Results

395.0ms

8384×

body

valid