Details

sample198.0ms

Algorithm

intervals

Results

88.0ms	1343×	body	80	nan
36.0ms	440×	body	80	valid

simplify52.0ms

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: 0.1b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite34.0ms

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:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
13.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series395.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- t 1.0) (log a))
39.0ms	(* y (log z))
119.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
175.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

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

prune320.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

localize23.0ms

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))))
0.3b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.1b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
86×	`add-sqr-sqrt`
82×	`add-cube-cbrt` `*-un-lft-identity`
65×	`unpow-prod-down`
37×	`add-exp-log`
26×	`log-prod`
24×	`div-exp`
19×	`add-cbrt-cube`
18×	`exp-sum` `associate-/l*`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
9×	`associate-r` `associate-l` `prod-exp` `div-inv`
8×	`pow-exp`
7×	`associate-/r*`
6×	`log-pow`
5×	`cbrt-undiv` `sqr-pow`
4×	`cbrt-unprod` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `log-rec` `pow-prod-down` `clear-num` `*-commutative` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate-*r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 205

Calls

4 calls:

16.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
7.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
20.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series757.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
41.0ms	(* y (log (/ 1 z)))
68.0ms	(* (log (/ 1 a)) t)
350.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify104.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	922	3387
1	3977	2970
2	5002	2953

prune663.0ms

Filtered

217 candidates to 142 candidates (65.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	217	6	223

Merged error: 0.0b

Counts

223 → 6

localize19.0ms

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))))
0.3b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
5.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

rewrite196.0ms

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))))
6.0ms	(* y (log (/ 1 z)))
4.0ms	(* (log (/ 1 a)) t)
46.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

series944.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
41.0ms	(* y (log (/ 1 z)))
65.0ms	(* (log (/ 1 a)) t)
540.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

simplify330.0ms

Algorithm

egg-herbie

Counts

1239 → 1239

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	34598

prune5.4s

Filtered

1239 candidates to 954 candidates (77.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1238	1	1239
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	1240	5	1245

Merged error: 0b

Counts

1245 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
0.8b	(/ (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

1075×	`times-frac`
432×	`sqrt-prod`
389×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
312×	`unpow-prod-down`
107×	`div-inv`
102×	`exp-sum`
75×	`associate-/l*`
24×	`sqr-pow`
22×	`add-exp-log`
14×	`add-cbrt-cube`
9×	`cbrt-undiv` `cbrt-prod` `div-exp`
5×	`associate-/r*`
4×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow1/3`
1×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r/` `associate-/l/`

Counts

4 → 510

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
43.0ms	(/ (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt y)
193.0ms	(cbrt y)
190.0ms	(cbrt y)
532.0ms	(/ (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x))))

simplify181.0ms

Algorithm

egg-herbie

Counts

522 → 522

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2316	18112
1	5002	17297

prune3.1s

Filtered

522 candidates to 370 candidates (70.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	522	0	522
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	522	5	527

Merged error: 0b

Counts

527 → 5

regimes262.0ms

Accuracy

0% (1.2b remaining)

Error of 1.4b against oracle of 0.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	39
1	36	39

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.0s	45998×	body	80	nan
1.2s	15178×	body	80	valid