Details

analyze860.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

sample108.0ms

Algorithm

intervals

Results

33.0ms	472×	body	80	nan
19.0ms	256×	body	80	valid
17.0ms	232×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5079	16

prune16.0ms

Filtered

1 candidates to 1 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: 0.2b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.7b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite31.0ms

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` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `exp-sum` `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 → 94

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

series206.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- t 1.0) (log a))
12.0ms	(* y (log z))
76.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
104.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify30.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5016	1237

prune182.0ms

Filtered

76 candidates to 106 candidates (-39.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 0.0b

Counts

108 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (* (pow z y) (pow a (- t 1.0))))
1.0b	(pow (pow (exp (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
1.4b	(cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.7b	(/ (* x (pow (pow (exp (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))) y)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
15×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`pow-exp` `prod-exp`
11×	`add-cube-cbrt`
10×	`cbrt-prod` `pow-to-exp` `unpow-prod-down` `rem-log-exp`
9×	`add-cbrt-cube`
8×	`pow-unpow`
6×	`div-exp`
5×	`pow1`
4×	`add-log-exp`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `cbrt-div` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`log-div` `log-prod` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `associate-r/` `clear-num` `log-pow` `flip--` `cbrt-unprod` `div-inv` `associate-/l` `pow-sub`

Counts

4 → 88

Calls

4 calls:

5.0ms	(log (* (pow z y) (pow a (- t 1.0))))
12.0ms	(pow (pow (exp (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
6.0ms	(cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
13.0ms	(/ (* x (pow (pow (exp (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))) y)

series6.7s

Counts

4 → 12

Calls

4 calls:

38.0ms	(log (* (pow z y) (pow a (- t 1.0))))
2.1s	(pow (pow (exp (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
228.0ms	(cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
4.4s	(/ (* x (pow (pow (exp (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (log (* (pow z y) (pow a (- t 1.0)))) b))) (cbrt (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))) y)

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5182	7019

prune742.0ms

Filtered

78 candidates to 100 candidates (-28.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Merged error: 0.0b

Counts

108 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow a (- t 1.0))
0.2b	(/ (pow a (- t 1.0)) (exp b))
0.5b	(* (pow z y) (/ (pow a (- t 1.0)) (exp b)))
1.7b	(/ (* x (* (pow z y) (/ (pow a (- t 1.0)) (exp b)))) y)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log` `add-sqr-sqrt`
60×	`times-frac`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
37×	`prod-exp`
35×	`div-exp`
34×	`unpow-prod-down`
28×	`associate-r`
25×	`add-cbrt-cube`
16×	`pow-to-exp` `pow-exp` `sqr-pow`
12×	`unswap-sqr`
9×	`associate-/l*`
8×	`unpow-prod-up` `sub-neg`
7×	`cbrt-undiv` `associate-l` `cbrt-unprod`
6×	`associate-/r*`
5×	`pow1` `pow-unpow`
4×	`add-log-exp`
3×	`associate-*r/` `div-inv`
2×	`frac-2neg` `clear-num` `associate-/l/` `pow-sub`
1×	`pow-pow` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 177

Calls

4 calls:

4.0ms	(pow a (- t 1.0))
6.0ms	(/ (pow a (- t 1.0)) (exp b))
13.0ms	(* (pow z y) (/ (pow a (- t 1.0)) (exp b)))
13.0ms	(/ (* x (* (pow z y) (/ (pow a (- t 1.0)) (exp b)))) y)

series162.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow a (- t 1.0))
22.0ms	(/ (pow a (- t 1.0)) (exp b))
54.0ms	(* (pow z y) (/ (pow a (- t 1.0)) (exp b)))
74.0ms	(/ (* x (* (pow z y) (/ (pow a (- t 1.0)) (exp b)))) y)

simplify72.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4976	2754
1	4976	2754

prune253.0ms

Filtered

128 candidates to 189 candidates (-47.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	190	7	197

Merged error: 0.0b

Counts

197 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow a (- t 1.0))
0.3b	(/ (exp b) (pow a (- t 1.0)))
0.4b	(* (/ (exp b) (pow a (- t 1.0))) (/ y (pow z y)))
1.7b	(/ x (* (/ (exp b) (pow a (- t 1.0))) (/ y (pow z y))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
97×	`add-exp-log`
96×	`times-frac`
68×	`div-exp`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
41×	`unpow-prod-down`
36×	`add-cbrt-cube`
32×	`prod-exp`
29×	`associate-l`
25×	`associate-r`
19×	`sqr-pow`
18×	`pow-to-exp` `pow-exp`
16×	`unswap-sqr`
14×	`cbrt-undiv`
9×	`associate-/r*`
8×	`unpow-prod-up` `sub-neg` `cbrt-unprod`
7×	`pow1`
6×	`associate-/l*`
5×	`pow-unpow` `associate-/r/`
4×	`div-inv` `add-log-exp`
3×	`pow-sub`
2×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`pow-pow` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 215

Calls

4 calls:

4.0ms	(pow a (- t 1.0))
6.0ms	(/ (exp b) (pow a (- t 1.0)))
22.0ms	(* (/ (exp b) (pow a (- t 1.0))) (/ y (pow z y)))
13.0ms	(/ x (* (/ (exp b) (pow a (- t 1.0))) (/ y (pow z y))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow a (- t 1.0))
23.0ms	(/ (exp b) (pow a (- t 1.0)))
81.0ms	(* (/ (exp b) (pow a (- t 1.0))) (/ y (pow z y)))
76.0ms	(/ x (* (/ (exp b) (pow a (- t 1.0))) (/ y (pow z y))))

simplify82.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5036	3670

prune263.0ms

Filtered

158 candidates to 227 candidates (-43.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	227	7	234

Merged error: 0b

Counts

234 → 7

regimes1.1s

Accuracy

15.7% (1.7b remaining)

Error of 1.7b against oracle of 0.0b and baseline of 2.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	53
1	57	53

end0.0ms

sample3.1s

Algorithm

intervals

Results

948.0ms	14183×	body	80	nan
631.0ms	8000×	body	80	valid
550.0ms	7055×	body	80	invalid

Details

analyze860.0ms

sample108.0ms

simplify38.0ms

prune16.0ms

localize18.0ms

rewrite31.0ms

series206.0ms

simplify30.0ms

prune182.0ms

localize32.0ms

rewrite38.0ms

series6.7s

simplify61.0ms

prune742.0ms

localize14.0ms

rewrite43.0ms

series162.0ms

simplify72.0ms

prune253.0ms

localize14.0ms

rewrite55.0ms

series192.0ms

simplify82.0ms

prune263.0ms

regimes1.1s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample3.1s

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