Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	231×	body	80	valid
1.0ms	13×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	16×	body	160	valid
1.0ms	6×	body	1280	valid
0.0ms	1×	body	2560	valid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
3.7b	(- (+ x y) (/ (* (- z t) y) (- a t)))
12.9b	(/ (* (- z t) y) (- a t))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

20.0ms	(* (- z t) y)
48.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
21.0ms	(/ (* (- z t) y) (- a t))

series181.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- z t) y)
98.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
56.0ms	(/ (* (- z t) y) (- a t))

simplify49.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune192.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
4.2b	(- (+ x y) (* (- z t) (/ y (- a t))))
9.7b	(* (- z t) (/ y (- a t)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 107

Calls

3 calls:

10.0ms	(/ y (- a t))
40.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
44.0ms	(* (- z t) (/ y (- a t)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ y (- a t))
100.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
58.0ms	(* (- z t) (/ y (- a t)))

simplify73.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	559	844
1	2676	803
2	5001	803

prune287.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (- a t))
0.0b	(+ x (- y (* (- z t) (/ y (- a t)))))
4.6b	(- y (* (- z t) (/ y (- a t))))
9.7b	(* (- z t) (/ y (- a t)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
31×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`flip3--` `associate-l` `associate-/r*` `flip--`
4×	`associate-/r/`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `associate-+r+` `diff-log` `div-exp` `associate-*l/` `prod-exp` `sum-log` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+` `distribute-lft-out`

Counts

4 → 111

Calls

4 calls:

10.0ms	(/ y (- a t))
11.0ms	(+ x (- y (* (- z t) (/ y (- a t)))))
5.0ms	(- y (* (- z t) (/ y (- a t))))
43.0ms	(* (- z t) (/ y (- a t)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ y (- a t))
99.0ms	(+ x (- y (* (- z t) (/ y (- a t)))))
73.0ms	(- y (* (- z t) (/ y (- a t))))
58.0ms	(* (- z t) (/ y (- a t)))

simplify53.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	408	708
1	1754	669
2	5002	669

prune309.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
7.5b	(- y (* (- z t) (* y (/ 1 (- a t)))))
9.7b	(* (- z t) (* y (/ 1 (- a t))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-l` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `associate-*r/` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`frac-times` `pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`associate-l/` `-commutative` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 129

Calls

4 calls:

12.0ms	(/ 1 (- a t))
30.0ms	(* y (/ 1 (- a t)))
6.0ms	(- y (* (- z t) (* y (/ 1 (- a t)))))
53.0ms	(* (- z t) (* y (/ 1 (- a t))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (- a t))
27.0ms	(* y (/ 1 (- a t)))
75.0ms	(- y (* (- z t) (* y (/ 1 (- a t)))))
56.0ms	(* (- z t) (* y (/ 1 (- a t))))

simplify53.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	422	742
1	1829	638
2	5002	592

prune281.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

regimes321.0ms

Accuracy

-2.7% (5.8b remaining)

Error of 9.8b against oracle of 4.0b and baseline of 9.7b

bsearch51.0ms

Steps

Iters	Range		Point
2	3.147991408827441	3.618674152218468	3.2068267517513194
8	-1.5936488927856455e-182	-3.211873688391442e-185	-7.228876828185814e-183

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	34
1	38	34

end0.0ms

sample726.0ms

Algorithm

intervals

Results

237.0ms	7395×	body	80	valid
51.0ms	450×	body	640	valid
40.0ms	401×	body	320	valid
34.0ms	227×	body	1280	valid
16.0ms	278×	body	160	valid
2.0ms	11×	body	2560	valid