Details

sample23.0ms

Algorithm

intervals

Results

8.0ms	242×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	7×	body	640	valid
0.0ms	8×	body	160	valid
0.0ms	3×	body	1280	valid

simplify130.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.1b	(/ (* (- z t) y) (- a t))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

28.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series171.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
59.0ms	(/ (* (- z t) y) (- a t))

simplify38.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	333	376
1	1377	346
2	5001	344

prune139.0ms

Filtered

54 candidates to 39 candidates (72.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.8b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.3b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
66.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
18.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- a t))
143.0ms	(cbrt (- a t))
96.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
111.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5002	1498

prune450.0ms

Filtered

139 candidates to 104 candidates (74.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a t)))
0.6b	(cbrt (cbrt (- a t)))
3.8b	(* (/ (- z t) (* (cbrt (- a t)) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
6.8b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

rewrite581.0ms

Algorithm

rewrite-expression-head

Rules

388×	`cbrt-div`
139×	`frac-times`
112×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
53×	`associate-*r/`
49×	`add-exp-log`
47×	`associate-*l/`
45×	`add-sqr-sqrt`
42×	`cbrt-prod`
37×	`*-un-lft-identity`
31×	`times-frac`
30×	`associate-r` `add-cbrt-cube`
25×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 210

Calls

4 calls:

2.0ms	(cbrt (cbrt (- a t)))
3.0ms	(cbrt (cbrt (- a t)))
531.0ms	(* (/ (- z t) (* (cbrt (- a t)) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
21.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (cbrt (- a t)))
148.0ms	(cbrt (cbrt (- a t)))
99.0ms	(* (/ (- z t) (* (cbrt (- a t)) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
111.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	1194	4395
1	4868	3508
2	5001	3486

prune1.2s

Filtered

222 candidates to 195 candidates (87.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt (cbrt (- a t)))
0.7b	(pow (cbrt (cbrt (- a t))) 3)
7.0b	(- (+ x y) (* (* (/ (- z t) (cbrt (- a t))) (/ (/ (* (cbrt y) (cbrt y)) (cbrt 1)) (pow (cbrt (cbrt (- a t))) 3))) (/ (cbrt y) (cbrt (- a t)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-prod`
20×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt` `frac-sub`
11×	`unpow-prod-down` `cube-prod`
10×	`frac-times` `associate-*l/`
9×	`add-log-exp`
8×	`cbrt-div`
7×	`flip3-+` `flip-+`
6×	`associate-*r/`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`pow-unpow` `flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`cube-div` `pow-pow` `diff-log`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow3` `pow-exp` `associate--l+` `sum-log` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 99

Calls

4 calls:

0.0ms	(cbrt y)
3.0ms	(cbrt (cbrt (- a t)))
6.0ms	(pow (cbrt (cbrt (- a t))) 3)
20.0ms	(- (+ x y) (* (* (/ (- z t) (cbrt (- a t))) (/ (/ (* (cbrt y) (cbrt y)) (cbrt 1)) (pow (cbrt (cbrt (- a t))) 3))) (/ (cbrt y) (cbrt (- a t)))))

series728.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt y)
174.0ms	(cbrt (cbrt (- a t)))
206.0ms	(pow (cbrt (cbrt (- a t))) 3)
168.0ms	(- (+ x y) (* (* (/ (- z t) (cbrt (- a t))) (/ (/ (* (cbrt y) (cbrt y)) (cbrt 1)) (pow (cbrt (cbrt (- a t))) 3))) (/ (cbrt y) (cbrt (- a t)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	736	1432
1	2976	1280
2	5001	1260

prune394.0ms

Filtered

111 candidates to 66 candidates (59.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.0b

regimes286.0ms

Accuracy

28.1% (4.9b remaining)

Error of 8.7b against oracle of 3.8b and baseline of 10.6b

bsearch52.0ms

Steps

Iters	Range		Point
0	3.2223289845859603e-186	3.311604597174445e-186	3.2669667908802025e-186
8	-9.739317299491343e-201	-2.5656855379612077e-203	-6.349456171606288e-201

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	25
1	42	25

end0.0ms

sample650.0ms

Algorithm

intervals

Results

245.0ms	7402×	body	80	valid
56.0ms	426×	body	640	valid
38.0ms	250×	body	1280	valid
35.0ms	391×	body	320	valid
14.0ms	239×	body	160	valid
3.0ms	16×	body	2560	valid