Details

sample31.0ms

Algorithm

intervals

Results

15.0ms

506×

body

valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	6
1	50	6
2	159	6
3	351	6
4	609	6
5	733	6
6	1068	6
7	1342	6
8	1506	6
9	1553	6
10	1553	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.2b	(* (* y 4.0) (- (* z z) t))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `sub-neg`
4×	`distribute-rgt-in` `add-cube-cbrt` `-un-lft-identity` `distribute-lft-in` `associate-r*` `associate--r+`
3×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 54

Calls

3 calls:

7.0ms	(- (* z z) t)
4.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
8.0ms	(* (* y 4.0) (- (* z z) t))

series160.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(- (* z z) t)
77.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
62.0ms	(* (* y 4.0) (- (* z z) t))

simplify46.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	292	385
1	1348	342
2	5001	337

prune140.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t))))
3.0b	(+ (- (* t t)) (pow z 4))
6.2b	(* (* y 4.0) (/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t)))
26.9b	(/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-exp-log` `associate-r` `add-cbrt-cube`
10×	`add-log-exp`
9×	`pow1`
8×	`distribute-lft-out`
6×	`prod-exp` `cbrt-unprod`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r*`
2×	`neg-sub0` `associate-+l-` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-r/` `associate-l` `neg-log` `clear-num` `-commutative` `flip--`

Counts

4 → 100

Calls

4 calls:

3.0ms	(- (* x x) (* (* y 4.0) (/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t))))
9.0ms	(+ (- (* t t)) (pow z 4))
14.0ms	(* (* y 4.0) (/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t)))
11.0ms	(/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t))

series476.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(- (* x x) (* (* y 4.0) (/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t))))
57.0ms	(+ (- (* t t)) (pow z 4))
154.0ms	(* (* y 4.0) (/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t)))
83.0ms	(/ (+ (- (* t t)) (pow z 4)) (+ (* z z) t))

simplify87.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	506	1228
1	2909	1037
2	5002	1022

prune331.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow x 2) (* 4.0 (* t y)))
0.0b	(* 4.0 (* t y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

2 → 29

Calls

2 calls:

5.0ms	(+ (pow x 2) (* 4.0 (* t y)))
5.0ms	(* 4.0 (* t y))

series61.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ (pow x 2) (* 4.0 (* t y)))
19.0ms	(* 4.0 (* t y))

simplify88.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	156	160
1	611	141
2	2603	141
3	5002	141

prune84.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* t y))))
0.2b	(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* t y)))
0.4b	(* (cbrt 4.0) (* t y))
1.0b	(* (cbrt 4.0) (cbrt 4.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1`
32×	`add-exp-log`
22×	`add-sqr-sqrt`
20×	`pow-prod-down`
19×	`cbrt-prod` `prod-exp` `cbrt-unprod`
18×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
8×	`associate-r`
6×	`pow1/3` `swap-sqr` `add-log-exp`
4×	`unswap-sqr`
3×	`*-commutative`
2×	`pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(+ (pow x 2) (* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* t y))))
15.0ms	(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* t y)))
5.0ms	(* (cbrt 4.0) (* t y))
6.0ms	(* (cbrt 4.0) (cbrt 4.0))

series211.0ms

Counts

4 → 10

Calls

4 calls:

89.0ms	(+ (pow x 2) (* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* t y))))
75.0ms	(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* t y)))
47.0ms	(* (cbrt 4.0) (* t y))
0.0ms	(* (cbrt 4.0) (cbrt 4.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	308	713
1	1513	576
2	5002	534

prune224.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

regimes529.0ms

Accuracy

86% (0.5b remaining)

Error of 2.9b against oracle of 2.4b and baseline of 5.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample851.0ms

Algorithm

intervals

Results

471.0ms

15668×

body

valid