Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	232×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	9×	body	160	valid

simplify121.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.1b	(- (+ x y) (/ (* (- z t) y) (- a t)))
12.3b	(/ (* (- z t) y) (- a t))

rewrite27.0ms

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:

6.0ms	(* (- z t) y)
10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series210.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* (- z t) y)
115.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
65.0ms	(/ (* (- z t) y) (- a t))

simplify51.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (12.0ms)

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

prune210.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.7b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.5b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite49.0ms

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:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
31.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series522.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- a t))
151.0ms	(cbrt (- a t))
101.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
118.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (80.0ms)

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

prune494.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
3.1b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
3.6b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `frac-times` `-un-lft-identity` `associate-r/`
14×	`associate-l` `frac-sub`
9×	`pow1` `add-cube-cbrt` `associate-*l/` `add-log-exp`
8×	`times-frac`
7×	`flip3-+` `flip-+`
6×	`cbrt-div`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `diff-log` `associate-/r/`
1×	`sub-neg` `associate-r` `associate--l+` `sum-log` `*-commutative` `div-inv`

Counts

4 → 120

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
32.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
7.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (- z t))
147.0ms	(cbrt (- z t))
105.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
120.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	796	2499
1	3082	2071
2	5001	1925

prune399.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
3.1b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
5.2b	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `associate-*l/` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
32.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
5.0ms	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- z t))
149.0ms	(cbrt (- z t))
102.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
87.0ms	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	621	1977
1	2350	1562
2	5001	1406

prune326.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.7b

regimes355.0ms

Accuracy

22.3% (4.2b remaining)

Error of 8.1b against oracle of 4.0b and baseline of 9.3b

bsearch103.0ms

Steps

Iters	Range		Point
8	5.385739917940565e-230	1.1813773243082582e-225	5.378243101833397e-226
10	-4.8761433142178394e-144	-6.29432788832743e-157	-1.367486021070251e-151

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample682.0ms

Algorithm

intervals

Results

257.0ms	7284×	body	80	valid
65.0ms	465×	body	640	valid
46.0ms	264×	body	1280	valid
39.0ms	402×	body	320	valid
18.0ms	260×	body	160	valid
4.0ms	22×	body	2560	valid