Details

sample33.0ms

Algorithm

intervals

Results

18.0ms

280×

body

valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	5
1	34	5
2	55	5
3	93	5
4	149	5
5	184	5
6	202	5
7	229	5
8	280	5
9	372	5
10	465	5
11	768	5
12	876	5
13	878	5
14	878	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 2.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
2.7b	(* y (/ (- z t) (- a t)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`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×	`flip3--` `associate-l` `flip--`
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 → 113

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- a t))))
8.0ms	(/ (- z t) (- a t))
12.0ms	(* y (/ (- z t) (- a t)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(+ x (* y (/ (- z t) (- a t))))
46.0ms	(/ (- z t) (- a t))
69.0ms	(* y (/ (- z t) (- a t)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	421	747
1	1657	704
2	5001	704

prune258.0ms

Filtered

122 candidates to 83 candidates (68.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	8	123

Merged error: 0.0b

Counts

123 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* y (* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t)))))
5.1b	(cbrt (/ (- z t) (- a t)))
5.1b	(cbrt (/ (- z t) (- a t)))
5.1b	(cbrt (/ (- z t) (- a t)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
38×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1` `add-exp-log`
7×	`cbrt-div` `add-cbrt-cube`
6×	`associate-/r/`
4×	`associate-*r/` `add-log-exp`
3×	`flip3--` `pow1/3` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `div-inv`
1×	`frac-times` `associate-r` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

20.0ms	(* y (* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t)))))
7.0ms	(cbrt (/ (- z t) (- a t)))
7.0ms	(cbrt (/ (- z t) (- a t)))
7.0ms	(cbrt (/ (- z t) (- a t)))

series1.1s

Counts

4 → 12

Calls

4 calls:

159.0ms	(* y (* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t)))))
324.0ms	(cbrt (/ (- z t) (- a t)))
309.0ms	(cbrt (/ (- z t) (- a t)))
311.0ms	(cbrt (/ (- z t) (- a t)))

simplify137.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	449	1623
1	1091	1553
2	3946	1540
3	5001	1510

prune474.0ms

Filtered

154 candidates to 110 candidates (71.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	153	9	162

Merged error: 0.0b

Counts

162 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.8b	(* (* (cbrt y) (cbrt y)) (* (cbrt y) (/ (- z t) (- a t))))
2.2b	(* (cbrt y) (/ (- z t) (- a t)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
32×	`associate-r`
30×	`add-exp-log`
27×	`times-frac`
19×	`add-cube-cbrt`
18×	`pow1` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
11×	`cbrt-prod`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow-prod-down`
7×	`associate-l`
4×	`add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `associate-*r/` `div-exp`
2×	`pow1/3` `associate-/r/` `*-commutative`
1×	`flip3--` `flip--` `div-inv`

Counts

4 → 104

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
15.0ms	(* (* (cbrt y) (cbrt y)) (* (cbrt y) (/ (- z t) (- a t))))
15.0ms	(* (cbrt y) (/ (- z t) (- a t)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt y)
190.0ms	(cbrt y)
93.0ms	(* (* (cbrt y) (cbrt y)) (* (cbrt y) (/ (- z t) (- a t))))
184.0ms	(* (cbrt y) (/ (- z t) (- a t)))

simplify69.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	382	805
1	1797	651
2	5002	619

prune245.0ms

Filtered

116 candidates to 74 candidates (63.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	116	9	125

Merged error: 0.0b

Counts

125 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
5.1b	(cbrt (/ (- z t) (- a t)))
6.4b	(/ (* y (* (cbrt (- z t)) (cbrt (- z t)))) (* (cbrt (- a t)) (cbrt (- a t))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
62×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
39×	`cbrt-div`
27×	`add-exp-log`
26×	`times-frac`
24×	`add-cube-cbrt`
20×	`flip3--` `flip--`
17×	`distribute-lft-out--`
15×	`add-cbrt-cube` `difference-of-squares`
14×	`associate-*r/`
12×	`frac-times`
11×	`pow1`
10×	`swap-sqr` `prod-exp` `associate-/r/` `cbrt-unprod`
8×	`pow1/3` `associate-r` `associate-l` `associate-/l/`
6×	`cbrt-undiv` `div-exp` `associate-*l/`
4×	`add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 152

Calls

4 calls:

3.0ms	(cbrt (- z t))
16.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
6.0ms	(cbrt (/ (- z t) (- a t)))
21.0ms	(/ (* y (* (cbrt (- z t)) (cbrt (- z t)))) (* (cbrt (- a t)) (cbrt (- a t))))

series788.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (- z t))
124.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
317.0ms	(cbrt (/ (- z t) (- a t)))
190.0ms	(/ (* y (* (cbrt (- z t)) (cbrt (- z t)))) (* (cbrt (- a t)) (cbrt (- a t))))

simplify125.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	834	1655
1	3482	1500
2	5001	1432

prune529.0ms

Filtered

164 candidates to 112 candidates (68.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	164	9	173

Merged error: 0.0b

Counts

173 → 9

regimes365.0ms

Accuracy

68.9% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 1.5b

bsearch84.0ms

Steps

Iters	Range		Point
9	6.056511580473963e-105	2.513454972484143e-99	1.7883278228757425e-99
8	-1.7279404347794328e+40	-3.1399871291003827e+37	-3.3292037274585957e+37

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample581.0ms

Algorithm

intervals

Results

319.0ms	8735×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

Iter	Nodes	Cost
0	20	5
1	34	5
2	55	5
3	93	5
4	149	5
5	184	5
6	202	5
7	229	5
8	280	5
9	372	5
10	465	5
11	768	5
12	876	5
13	878	5
14	878	5

Iter	Nodes	Cost
0	20	5
1	34	5
2	55	5
3	93	5
4	149	5
5	184	5
6	202	5
7	229	5
8	280	5
9	372	5
10	465	5
11	768	5
12	876	5
13	878	5
14	878	5

Iter	Nodes	Cost
0	20	5
1	34	5
2	55	5
3	93	5
4	149	5
5	184	5
6	202	5
7	229	5
8	280	5
9	372	5
10	465	5
11	768	5
12	876	5
13	878	5
14	878	5