Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	246×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	7×	body	160	valid
0.0ms	2×	body	2560	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.0b	(/ (* (- y x) (- z t)) (- a t))

rewrite52.0ms

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:

15.0ms	(* (- y x) (- z t))
12.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
20.0ms	(/ (* (- y x) (- z t)) (- a t))

series321.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (- y x) (- z t))
157.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
129.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune258.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.9b	(* (- y x) (/ (- z t) (- a t)))
2.0b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite33.0ms

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:

8.0ms	(/ (- z t) (- a t))
16.0ms	(* (- y x) (/ (- z t) (- a t)))
4.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series341.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- z t) (- a t))
120.0ms	(* (- y x) (/ (- z t) (- a t)))
168.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify56.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune323.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ z (- a t))
0.0b	(/ t (- a t))
1.9b	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
2.0b	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 142

Calls

4 calls:

9.0ms	(/ z (- a t))
5.0ms	(/ t (- a t))
34.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
7.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ z (- a t))
45.0ms	(/ t (- a t))
118.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
157.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	581	1057
1	2586	1012
2	5002	1012

prune431.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.0b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.1b	(/ (- y x) (/ (- a t) (- z t)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

8.0ms	(/ (- a t) (- z t))
45.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
16.0ms	(/ (- y x) (/ (- a t) (- z t)))

series434.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- a t) (- z t))
160.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
221.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify109.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5003	2984

prune638.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.4b

regimes228.0ms

Accuracy

10.5% (6.6b remaining)

Error of 10.7b against oracle of 4.1b and baseline of 11.5b

bsearch222.0ms

Steps

Iters	Range		Point
6	1.945658225909592e-97	1.6136504421647031e-96	5.696562570285325e-97
10	2.3640854339019394e-185	5.384026678480704e-172	2.4352685801940737e-178
10	1.2576615377335737e-286	5.729655012942905e-273	5.6477842289868e-273
10	-4.8761433142178394e-144	-9.84192585673944e-162	-2.8452776584917417e-147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	31
1	40	31

end0.0ms

sample737.0ms

Algorithm

intervals

Results

291.0ms	7786×	body	80	valid
61.0ms	455×	body	640	valid
49.0ms	427×	body	320	valid
41.0ms	248×	body	1280	valid
19.0ms	275×	body	160	valid
4.0ms	18×	body	2560	valid