Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	258×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	2×	body	160	valid

simplify70.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
0.7b	(+ x (/ (* (- y x) (- z t)) (- a t)))
15.5b	(/ (* (- y x) (- z t)) (- a t))

rewrite90.0ms

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:

36.0ms	(* (- y x) (- z t))
20.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
31.0ms	(/ (* (- y x) (- z t)) (- a t))

series271.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- y x) (- z t))
139.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
101.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune223.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
0.7b	(+ x (* (- y x) (/ (- z t) (- a t))))
1.9b	(* (- y x) (/ (- z t) (- a t)))

rewrite95.0ms

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:

21.0ms	(/ (- z t) (- a t))
9.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
59.0ms	(* (- y x) (/ (- z t) (- a t)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (- z t) (- a t))
137.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
101.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

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

prune263.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.7b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.1b	(/ (- y x) (/ (- a t) (- z t)))

rewrite169.0ms

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:

21.0ms	(/ (- a t) (- z t))
88.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
43.0ms	(/ (- y x) (/ (- a t) (- z t)))

series399.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (- a t) (- z t))
140.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
215.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify97.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (20.0ms)

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

prune633.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.1b	(/ (- y x) (* (* (cbrt (- a t)) (cbrt (- a t))) (/ (cbrt (- a t)) (- z t))))
5.8b	(+ x (/ (- y x) (* (* (cbrt (- a t)) (cbrt (- a t))) (/ (cbrt (- a t)) (- z t)))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
76.0ms	(/ (- y x) (* (* (cbrt (- a t)) (cbrt (- a t))) (/ (cbrt (- a t)) (- z t))))
55.0ms	(+ x (/ (- y x) (* (* (cbrt (- a t)) (cbrt (- a t))) (/ (cbrt (- a t)) (- z t)))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (- a t))
140.0ms	(cbrt (- a t))
185.0ms	(/ (- y x) (* (* (cbrt (- a t)) (cbrt (- a t))) (/ (cbrt (- a t)) (- z t))))
141.0ms	(+ x (/ (- y x) (* (* (cbrt (- a t)) (cbrt (- a t))) (/ (cbrt (- a t)) (- z t)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	654	1281
1	2183	1092
2	5003	1064

prune298.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.6b

regimes239.0ms

Accuracy

18.1% (6.4b remaining)

Error of 10.6b against oracle of 4.2b and baseline of 12.0b

bsearch80.0ms

Steps

Iters	Range		Point
9	1.2482730762301338e-167	1.8900198799241145e-159	1.2502224442482174e-160
8	-7.969332197827611e-102	-3.347036471636472e-105	-4.5026886998339375e-105

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample760.0ms

Algorithm

intervals

Results

234.0ms	7768×	body	80	valid
50.0ms	494×	body	640	valid
40.0ms	295×	body	1280	valid
34.0ms	412×	body	320	valid
14.0ms	261×	body	160	valid
3.0ms	18×	body	2560	valid