Details

sample221.0ms

Algorithm

intervals

Results

101.0ms	1551×	body	80	nan
38.0ms	503×	body	80	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.4b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `exp-sum` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 95

Calls

4 calls:

9.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series376.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
116.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
165.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify57.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	493	869
1	2033	715
2	5001	683

prune310.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Merged error: 0b

Counts

109 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
0.2b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
7.5b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

3180×	`times-frac`
1295×	`add-sqr-sqrt`
1291×	`add-cube-cbrt` `*-un-lft-identity`
793×	`unpow-prod-down`
256×	`exp-sum`
152×	`div-inv`
89×	`associate-/l*`
61×	`sqr-pow`
49×	`add-exp-log`
45×	`div-exp`
26×	`log-prod`
22×	`add-cbrt-cube`
17×	`associate-/r*`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1` `pow-exp`
9×	`cbrt-undiv` `associate-r` `associate-l`
6×	`log-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp`
2×	`pow-flip` `frac-2neg` `log-rec` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate-/r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 1227

Calls

4 calls:

16.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
48.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

series893.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
62.0ms	(* (log (/ 1 a)) t)
37.0ms	(* y (log (/ 1 z)))
509.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

simplify316.0ms

Algorithm

egg-herbie

Counts

1239 → 1239

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5001	34598

prune5.4s

Filtered

1239 candidates to 954 candidates (77.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1239	0	1239
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1239	5	1244

Merged error: 0b

Counts

1244 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* (pow a (- t 1.0)) (pow z y)))
0.1b	(pow a (- t 1.0))
1.4b	(/ (/ (* x (* (pow a (- t 1.0)) (pow z y))) (exp b)) y)
1.5b	(/ (* x (* (pow a (- t 1.0)) (pow z y))) (exp b))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log`
57×	`prod-exp`
36×	`times-frac`
34×	`div-exp`
32×	`add-cbrt-cube`
27×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`add-cube-cbrt`
19×	`pow-to-exp` `pow-exp`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
8×	`associate-/l*`
7×	`pow1`
6×	`associate-/r*` `div-inv`
5×	`pow-unpow`
4×	`add-log-exp`
3×	`unpow-prod-down` `associate-l` `pow-sub`
2×	`unpow-prod-up` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`
1×	`sub-neg` `pow-pow` `associate-r` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

8.0ms	(* x (* (pow a (- t 1.0)) (pow z y)))
4.0ms	(pow a (- t 1.0))
11.0ms	(/ (/ (* x (* (pow a (- t 1.0)) (pow z y))) (exp b)) y)
10.0ms	(/ (* x (* (pow a (- t 1.0)) (pow z y))) (exp b))

series668.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* x (* (pow a (- t 1.0)) (pow z y)))
73.0ms	(pow a (- t 1.0))
234.0ms	(/ (/ (* x (* (pow a (- t 1.0)) (pow z y))) (exp b)) y)
211.0ms	(/ (* x (* (pow a (- t 1.0)) (pow z y))) (exp b))

simplify84.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	693	1446
1	3254	1262
2	5001	1247

prune360.0ms

Filtered

150 candidates to 94 candidates (62.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	150	5	155

Merged error: 0b

Counts

155 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (/ (/ y x) (* (pow a (- t 1.0)) (pow z y))) (exp b)))
0.1b	(pow a (- t 1.0))
1.4b	(* (/ (/ y x) (* (pow a (- t 1.0)) (pow z y))) (exp b))
5.7b	(/ (/ y x) (* (pow a (- t 1.0)) (pow z y)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

314×	`add-exp-log`
194×	`div-exp`
174×	`prod-exp`
61×	`pow-to-exp` `pow-exp`
59×	`add-cbrt-cube`
56×	`times-frac`
35×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
24×	`cbrt-undiv`
22×	`rec-exp` `1-exp`
18×	`associate-l`
16×	`cbrt-unprod` `associate-/l*`
10×	`pow1`
6×	`div-inv`
5×	`pow-unpow`
4×	`associate-*l/` `add-log-exp`
3×	`unpow-prod-down` `associate-r` `associate-/r/` `pow-sub`
2×	`unpow-prod-up` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`sub-neg` `pow-pow` `*-commutative` `associate-/l/` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 236

Calls

4 calls:

15.0ms	(/ 1 (* (/ (/ y x) (* (pow a (- t 1.0)) (pow z y))) (exp b)))
4.0ms	(pow a (- t 1.0))
15.0ms	(* (/ (/ y x) (* (pow a (- t 1.0)) (pow z y))) (exp b))
10.0ms	(/ (/ y x) (* (pow a (- t 1.0)) (pow z y)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ 1 (* (/ (/ y x) (* (pow a (- t 1.0)) (pow z y))) (exp b)))
74.0ms	(pow a (- t 1.0))
205.0ms	(* (/ (/ y x) (* (pow a (- t 1.0)) (pow z y))) (exp b))
159.0ms	(/ (/ y x) (* (pow a (- t 1.0)) (pow z y)))

simplify108.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1024	2310
1	4544	2005
2	5001	2003

prune409.0ms

Filtered

248 candidates to 108 candidates (43.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	248	5	253

Merged error: 0b

Counts

253 → 5

regimes394.0ms

Accuracy

80.7% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 1.9b

bsearch342.0ms

Steps

Iters	Range		Point
7	304.0849354186872	8389.426513849796	8234.665933457405
8	-2.7372821165424347e+41	-3.2829900886244486e+38	-1.3375298747491056e+41

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	24
1	50	24

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.0s	45515×	body	80	nan
1.2s	15363×	body	80	valid