Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

281×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	5
1	35	5
2	56	5
3	94	5
4	150	5
5	185	5
6	203	5
7	230	5
8	280	5
9	368	5
10	457	5
11	723	5
12	922	5
13	1038	5
14	1060	5
15	1060	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: 1.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- z a))))
0.0b	(/ (- z t) (- z a))
1.8b	(* y (/ (- z t) (- z a)))

rewrite28.0ms

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) (- z a))))
7.0ms	(/ (- z t) (- z a))
13.0ms	(* y (/ (- z t) (- z a)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ x (* y (/ (- z t) (- z a))))
45.0ms	(/ (- z t) (- z a))
64.0ms	(* y (/ (- z t) (- z a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	423	747
1	1655	704
2	5001	704

prune249.0ms

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: 0b

Counts

123 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (* (- z t) (/ 1 (- z a)))))
0.0b	(/ 1 (- z a))
0.2b	(* (- z t) (/ 1 (- z a)))
1.8b	(* y (* (- z t) (/ 1 (- z a))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`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×	`frac-times` `pow-prod-down` `associate-*l/` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `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 → 130

Calls

4 calls:

3.0ms	(+ x (* y (* (- z t) (/ 1 (- z a)))))
5.0ms	(/ 1 (- z a))
13.0ms	(* (- z t) (/ 1 (- z a)))
12.0ms	(* y (* (- z t) (/ 1 (- z a))))

series219.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ x (* y (* (- z t) (/ 1 (- z a)))))
33.0ms	(/ 1 (- z a))
46.0ms	(* (- z t) (/ 1 (- z a)))
65.0ms	(* y (* (- z t) (/ 1 (- z a))))

simplify57.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	457	788
1	2015	679
2	5001	634

prune226.0ms

Filtered

142 candidates to 86 candidates (60.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	142	8	150

Merged error: 0b

Counts

150 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* y (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))))
4.0b	(cbrt (/ (- z t) (- z a)))
4.0b	(cbrt (/ (- z t) (- z a)))
4.0b	(cbrt (/ (- z t) (- z a)))

rewrite51.0ms

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:

24.0ms	(* y (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))))
7.0ms	(cbrt (/ (- z t) (- z a)))
7.0ms	(cbrt (/ (- z t) (- z a)))
7.0ms	(cbrt (/ (- z t) (- z a)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* y (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))))
122.0ms	(cbrt (/ (- z t) (- z a)))
127.0ms	(cbrt (/ (- z t) (- z a)))
155.0ms	(cbrt (/ (- z t) (- z a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	301	1464
1	651	1394
2	1651	1384
3	5001	1364

prune590.0ms

Filtered

154 candidates to 106 candidates (68.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	154	8	162

Merged error: 0b

Counts

162 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
50×	`times-frac`
46×	`associate-r`
42×	`cbrt-prod`
28×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`cbrt-div`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 136

Calls

4 calls:

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

series558.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (- z a))
143.0ms	(cbrt (- z a))
144.0ms	(cbrt (- z a))
108.0ms	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

simplify81.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	646	1592
1	3093	1439
2	5001	1374

prune388.0ms

Filtered

148 candidates to 113 candidates (76.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	148	8	156

Merged error: 0b

Counts

156 → 8

regimes288.0ms

Accuracy

58.6% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 1.3b

bsearch79.0ms

Steps

Iters	Range		Point
9	2.5275950713790557e-26	7.98514978676205e-20	4.593377905853265e-23
8	-1.2493295532820779e+48	-8.149194550109708e+43	-8.270128523654645e+43

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample578.0ms

Algorithm

intervals

Results

315.0ms	8728×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid