Details

sample37.0ms

Algorithm

intervals

Results

18.0ms

701×

body

valid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	4
1	41	4
2	102	4
3	228	4
4	411	4
5	786	4
6	2469	4
7	5002	4

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: 7.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
6.8b	(/ (* (cosh x) (/ y x)) z)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
103×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
78×	`add-cube-cbrt`
65×	`associate-r`
37×	`associate-/l*`
21×	`associate-/l/`
20×	`cosh-def`
18×	`frac-times` `associate-*r/`
16×	`add-exp-log` `add-cbrt-cube`
15×	`associate-l` `associate-/r*`
10×	`unswap-sqr`
7×	`clear-num`
6×	`div-inv`
5×	`cbrt-undiv` `frac-2neg` `div-exp` `*-commutative`
4×	`pow1` `prod-exp` `un-div-inv` `cbrt-unprod`
2×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down`

Counts

2 → 188

Calls

2 calls:

9.0ms	(* (cosh x) (/ y x))
14.0ms	(/ (* (cosh x) (/ y x)) z)

series193.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (cosh x) (/ y x))
115.0ms	(/ (* (cosh x) (/ y x)) z)

simplify103.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	805	1311
1	3568	1249
2	5002	1233

prune446.0ms

Filtered

194 candidates to 151 candidates (77.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	7	194
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	8	195

Merged error: 0b

Counts

195 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
5.4b	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

291×	`add-sqr-sqrt`
286×	`times-frac`
282×	`associate-r`
195×	`*-un-lft-identity`
180×	`associate-l`
145×	`add-cube-cbrt`
80×	`unswap-sqr`
52×	`*-commutative`
26×	`add-exp-log` `add-cbrt-cube`
25×	`distribute-lft-out`
22×	`associate-/r*`
13×	`associate-/l*`
10×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-log-exp`
4×	`associate-*l/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`associate-/l/`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `sum-log` `div-inv`

Counts

3 → 387

Calls

3 calls:

8.0ms	(+ (exp x) (exp (- x)))
7.0ms	(* (+ (exp x) (exp (- x))) y)
23.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (exp x) (exp (- x)))
55.0ms	(* (+ (exp x) (exp (- x))) y)
92.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

simplify123.0ms

Algorithm

egg-herbie

Counts

396 → 396

Iterations

Useful iterations: 1 (61.0ms)

Iter	Nodes	Cost
0	1774	5270
1	5002	5121

prune933.0ms

Filtered

396 candidates to 258 candidates (65.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	395	1	396
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	398	6	404

Merged error: 0b

Counts

404 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.6b	(cbrt z)
5.0b	(* (/ (* (cosh x) y) (* (cbrt z) (cbrt z))) (/ (/ 1 x) (cbrt z)))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

2267×	`add-sqr-sqrt`
1333×	`frac-times`
1260×	`associate-/r*`
1174×	`*-un-lft-identity`
1168×	`times-frac`
1134×	`add-cube-cbrt`
1091×	`associate-/l*`
1025×	`cbrt-prod`
769×	`associate-l`
523×	`associate-r`
487×	`unswap-sqr`
431×	`associate-/l/`
292×	`swap-sqr`
233×	`add-cbrt-cube`
122×	`clear-num`
120×	`frac-2neg` `cbrt-unprod`
119×	`add-exp-log`
118×	`*-commutative`
116×	`cbrt-undiv`
75×	`associate-*l/`
53×	`div-inv`
50×	`div-exp`
45×	`prod-exp`
32×	`cosh-def`
31×	`associate-*r/`
6×	`pow1` `un-div-inv`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`pow-prod-down`

Counts

4 → 2086

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
1.0ms	(cbrt z)
360.0ms	(* (/ (* (cosh x) y) (* (cbrt z) (cbrt z))) (/ (/ 1 x) (cbrt z)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt z)
179.0ms	(cbrt z)
188.0ms	(cbrt z)
136.0ms	(* (/ (* (cosh x) y) (* (cbrt z) (cbrt z))) (/ (/ 1 x) (cbrt z)))

simplify315.0ms

Algorithm

egg-herbie

Counts

2098 → 2098

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5002	31696

prune5.2s

Filtered

2098 candidates to 1329 candidates (63.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2098	0	2098
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	2098	6	2104

Merged error: 0b

Counts

2104 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (cosh x) y)
0.2b	(/ (/ 1 x) z)
6.1b	(* (* (cosh x) y) (/ (/ 1 x) z))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

169×	`times-frac`
139×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
107×	`add-cube-cbrt`
51×	`associate-/l*`
49×	`add-exp-log` `associate-r`
31×	`associate-*l/` `add-cbrt-cube`
30×	`cosh-def` `associate-/l/`
28×	`frac-times` `associate-*r/`
18×	`div-exp` `associate-l` `associate-/r*`
16×	`prod-exp`
14×	`unswap-sqr`
12×	`div-inv`
10×	`pow1` `cbrt-unprod`
9×	`cbrt-undiv`
8×	`clear-num`
6×	`frac-2neg` `un-div-inv`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `rec-exp` `1-exp` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

3 → 257

Calls

3 calls:

4.0ms	(* (cosh x) y)
11.0ms	(/ (/ 1 x) z)
28.0ms	(* (* (cosh x) y) (/ (/ 1 x) z))

series194.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (cosh x) y)
12.0ms	(/ (/ 1 x) z)
114.0ms	(* (* (cosh x) y) (/ (/ 1 x) z))

simplify52.0ms

Algorithm

egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1097	1776
1	5001	1574

prune503.0ms

Filtered

266 candidates to 170 candidates (63.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	266	6	272

Merged error: 0b

Counts

272 → 6

regimes143.0ms

Accuracy

94.5% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 7.2b

bsearch56.0ms

Steps

Iters	Range		Point
4	1.509871079665796e-52	2.264781558684953e-52	2.236171641711172e-52
5	-3.4658963496174327e-19	-1.077699933362376e-19	-3.411335329209465e-19

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

620.0ms

22369×

body

valid