Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	242×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	7×	body	160	valid

simplify66.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.2b	(+ x (/ (* (- y x) (- z t)) (- a t)))
16.1b	(/ (* (- y x) (- z t)) (- a t))

rewrite46.0ms

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:

17.0ms	(* (- y x) (- z t))
11.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
13.0ms	(/ (* (- y x) (- z t)) (- a t))

series286.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (- y x) (- z t))
144.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
107.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune226.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.2b	(+ x (/ (- y x) (/ (- a t) (- z t))))
3.4b	(/ (- y x) (/ (- a t) (- z t)))

rewrite120.0ms

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:

11.0ms	(/ (- a t) (- z t))
67.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
23.0ms	(/ (- y x) (/ (- a t) (- z t)))

series393.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- a t) (- z t))
152.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
193.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify104.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (25.0ms)

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

prune594.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.2b	(+ x (* (- y x) (/ (- z t) (- a t))))
3.5b	(* (- y x) (/ (- z t) (- a t)))

rewrite51.0ms

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))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
32.0ms	(* (- y x) (/ (- z t) (- a t)))

series304.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- z t) (- a t))
145.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
111.0ms	(* (- 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

prune317.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
1.2b	(/ (/ (- a t) (- z t)) (cbrt (- y x)))
2.7b	(/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x))))
9.0b	(+ x (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x)))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

1623×	`times-frac`
1162×	`*-un-lft-identity`
1160×	`add-sqr-sqrt`
475×	`cbrt-prod`
470×	`add-cube-cbrt`
345×	`distribute-lft-out--` `difference-of-squares`
262×	`associate-/r*`
57×	`associate-/r/`
35×	`flip3--` `flip--`
32×	`associate-/l*`
30×	`add-exp-log`
29×	`div-inv`
20×	`cbrt-div`
18×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
9×	`associate-/l/`
6×	`add-log-exp`
4×	`pow1` `frac-times`
3×	`prod-exp` `cbrt-unprod`
2×	`frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 872

Calls

4 calls:

2.0ms	(cbrt (- y x))
29.0ms	(/ (/ (- a t) (- z t)) (cbrt (- y x)))
62.0ms	(/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x))))
136.0ms	(+ x (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x)))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- y x))
169.0ms	(/ (/ (- a t) (- z t)) (cbrt (- y x)))
186.0ms	(/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x))))
151.0ms	(+ x (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x)))))

simplify158.0ms

Algorithm

egg-herbie

Counts

884 → 884

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2407	14747
1	5002	14663

prune2.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.2b

regimes294.0ms

Accuracy

20.1% (5.9b remaining)

Error of 10.1b against oracle of 4.2b and baseline of 11.6b

bsearch72.0ms

Steps

Iters	Range		Point
8	5.113248843062357e-172	2.5245095814102843e-169	5.599418233641363e-170
5	-6.603606594204675e-151	-2.909954061988625e-151	-3.494549615190394e-151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	12
1	31	12

end0.0ms

sample689.0ms

Algorithm

intervals

Results

254.0ms	7783×	body	80	valid
56.0ms	481×	body	640	valid
47.0ms	269×	body	1280	valid
37.0ms	386×	body	320	valid
17.0ms	278×	body	160	valid
3.0ms	18×	body	2560	valid