Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	252×	body	80	valid
1.0ms	13×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	8×	body	1280	valid
0.0ms	8×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.9b	(+ x (/ (* (- y x) (- z t)) (- a t)))
17.7b	(/ (* (- y x) (- z t)) (- a t))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

16.0ms	(* (- y x) (- z t))
10.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series334.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* (- y x) (- z t))
189.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
108.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify56.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune247.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.5b	(* (- y x) (/ (- z t) (- a t)))
1.9b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

11.0ms	(/ (- z t) (- a t))
37.0ms	(* (- y x) (/ (- z t) (- a t)))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series320.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- z t) (- a t))
113.0ms	(* (- y x) (/ (- z t) (- a t)))
158.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify55.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5001	820

prune289.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ z (- a t)) (/ t (- a t)))
0.0b	(/ t (- a t))
1.5b	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
1.9b	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
51×	`times-frac`
29×	`distribute-lft-out--`
20×	`add-cube-cbrt`
18×	`associate-r`
17×	`difference-of-squares`
14×	`flip3--` `flip--`
10×	`associate-/r/`
8×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `distribute-rgt-out--`
5×	`sub-neg` `associate-l` `associate-/r*` `div-inv`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*r/` `frac-sub` `sub-div`
3×	`associate-/l*`
2×	`associate-*l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

49.0ms	(- (/ z (- a t)) (/ t (- a t)))
5.0ms	(/ t (- a t))
153.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
15.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ z (- a t)) (/ t (- a t)))
44.0ms	(/ t (- a t))
108.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
163.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	547	1125
1	2404	1072
2	5001	1072

prune395.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- a t))
1.9b	(+ (+ x (* (/ z (- a t)) (- y x))) (* (- y x) (- (/ t (- a t)))))
3.1b	(* (- y x) (- (/ t (- a t))))
6.6b	(* (/ z (- a t)) (- y x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
61×	`times-frac`
51×	`associate-r`
44×	`add-cube-cbrt`
26×	`associate-l`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
15×	`distribute-lft-out--` `difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
10×	`frac-add`
9×	`distribute-neg-frac` `add-log-exp`
8×	`pow1` `frac-times` `associate-/r/`
7×	`associate-*l/`
6×	`flip3-+` `flip-+`
5×	`associate-r/` `associate-/r`
4×	`div-inv`
3×	`prod-exp` `sum-log` `distribute-rgt-neg-out` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative`
1×	`+-commutative` `neg-mul-1` `associate-+l+` `frac-2neg` `unsub-neg` `clear-num`

Counts

4 → 181

Calls

4 calls:

5.0ms	(/ t (- a t))
11.0ms	(+ (+ x (* (/ z (- a t)) (- y x))) (* (- y x) (- (/ t (- a t)))))
43.0ms	(* (- y x) (- (/ t (- a t))))
23.0ms	(* (/ z (- a t)) (- y x))

series419.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ t (- a t))
150.0ms	(+ (+ x (* (/ z (- a t)) (- y x))) (* (- y x) (- (/ t (- a t)))))
66.0ms	(* (- y x) (- (/ t (- a t))))
155.0ms	(* (/ z (- a t)) (- y x))

simplify111.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	886	1607
1	4662	1531
2	5001	1529

prune548.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

regimes296.0ms

Accuracy

36.8% (4.8b remaining)

Error of 9.1b against oracle of 4.2b and baseline of 11.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	36
1	55	36
2	56	36
3	56	36

end0.0ms

sample691.0ms

Algorithm

intervals

Results

255.0ms	7778×	body	80	valid
56.0ms	475×	body	640	valid
46.0ms	277×	body	1280	valid
37.0ms	387×	body	320	valid
18.0ms	301×	body	160	valid
2.0ms	11×	body	2560	valid