Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

278×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	5
1	36	4
2	59	4
3	103	4
4	173	4
5	236	4
6	265	4
7	311	4
8	375	4
9	511	4
10	674	4
11	1179	4
12	1300	4
13	1308	4
14	1308	4

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 1.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `flip3--` `fma-def` `associate-l` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `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 → 122

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- a t))))
9.0ms	(/ (- z t) (- a t))
18.0ms	(* y (/ (- z t) (- a t)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(+ x (* y (/ (- z t) (- a t))))
48.0ms	(/ (- z t) (- a t))
68.0ms	(* y (/ (- z t) (- a t)))

simplify56.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	433	776
1	1705	730
2	5002	730

prune294.0ms

Filtered

131 candidates to 92 candidates (70.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Merged error: 0b

Counts

132 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
16×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))

series626.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (- a t))
153.0ms	(cbrt (- z t))
159.0ms	(cbrt (- z t))
156.0ms	(cbrt (- z t))

simplify54.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	241	452
1	531	432
2	1470	420
3	5002	392

prune315.0ms

Filtered

80 candidates to 72 candidates (90.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	80	8	88

Merged error: 0b

Counts

88 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (* (- z t) (/ 1 (- a t)))))
0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
2.0b	(* y (* (- z t) (/ 1 (- a t))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
26×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-*l/` `associate-/r/` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `fma-def` `1-exp` `associate-/l*` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 141

Calls

4 calls:

4.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
6.0ms	(/ 1 (- a t))
14.0ms	(* (- z t) (/ 1 (- a t)))
13.0ms	(* y (* (- z t) (/ 1 (- a t))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
35.0ms	(/ 1 (- a t))
52.0ms	(* (- z t) (/ 1 (- a t)))
69.0ms	(* y (* (- z t) (/ 1 (- a t))))

simplify63.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	468	829
1	2047	715
2	5003	668

prune279.0ms

Filtered

153 candidates to 97 candidates (63.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	153	8	161

Merged error: 0b

Counts

161 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
3.5b	(cbrt (/ (- z t) (- a t)))
3.5b	(cbrt (/ (- z t) (- a t)))
3.5b	(cbrt (/ (- z t) (- a t)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

333×	`*-un-lft-identity`
277×	`cbrt-prod`
273×	`add-sqr-sqrt`
229×	`times-frac`
106×	`distribute-lft-out--`
93×	`add-cube-cbrt`
78×	`difference-of-squares`
58×	`swap-sqr`
34×	`associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3--` `flip--` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 284

Calls

4 calls:

38.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
7.0ms	(cbrt (/ (- z t) (- a t)))
8.0ms	(cbrt (/ (- z t) (- a t)))
7.0ms	(cbrt (/ (- z t) (- a t)))

series1.2s

Counts

4 → 12

Calls

4 calls:

271.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
322.0ms	(cbrt (/ (- z t) (- a t)))
314.0ms	(cbrt (/ (- z t) (- a t)))
316.0ms	(cbrt (/ (- z t) (- a t)))

simplify90.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	558	3688
1	1805	3618
2	5001	3416

prune777.0ms

Filtered

296 candidates to 188 candidates (63.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	296	8	304

Merged error: 0b

Counts

304 → 8

regimes318.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	19
1	19	19

end0.0ms

sample592.0ms

Algorithm

intervals

Results

321.0ms	8700×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid