Details

analyze1.8s

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
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

sample63.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
14.0ms	152×	body	80	nan

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5545	33

prune23.0ms

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: 4.3b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ t a)) t)
0.5b	(/ 2.0 (* t 3.0))
1.1b	(* z (/ (sqrt (+ t a)) t))
3.8b	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
47×	`times-frac`
45×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
29×	`sqrt-prod`
25×	`associate-r`
19×	`associate-*r/`
16×	`add-exp-log` `add-cbrt-cube`
14×	`frac-add`
10×	`associate-/l*`
8×	`frac-times` `flip3--` `flip--`
7×	`distribute-lft-out`
6×	`pow1` `frac-sub` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `associate-/r*`
3×	`associate-l` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`sub-neg` `associate-+r+` `frac-2neg` `sqrt-div` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 138

Calls

4 calls:

6.0ms	(/ (sqrt (+ t a)) t)
4.0ms	(/ 2.0 (* t 3.0))
11.0ms	(* z (/ (sqrt (+ t a)) t))
13.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (sqrt (+ t a)) t)
2.0ms	(/ 2.0 (* t 3.0))
16.0ms	(* z (/ (sqrt (+ t a)) t))
52.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4991	2716
1	4991	2716

prune297.0ms

Filtered

106 candidates to 150 candidates (-41.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	147	5	152

Merged error: 0.5b

Counts

152 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- b c) (- (/ 0.6666666666666666 t) (+ a (/ 5.0 6.0))))
0.2b	(/ (sqrt (+ t a)) t)
1.1b	(* z (/ (sqrt (+ t a)) t))
3.8b	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 0.6666666666666666 t) (+ a (/ 5.0 6.0)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
45×	`times-frac`
37×	`add-cube-cbrt`
32×	`associate-r`
29×	`sqrt-prod`
23×	`associate-*r/`
16×	`frac-times` `flip3--` `flip--`
14×	`frac-add`
13×	`add-exp-log` `add-cbrt-cube`
12×	`frac-sub`
8×	`pow1` `flip3-+` `associate-l` `flip-+` `distribute-lft-out`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`sub-neg` `associate-*l/` `unswap-sqr`
3×	`prod-exp` `associate-/r*` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `sqrt-div` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 157

Calls

4 calls:

19.0ms	(* (- b c) (- (/ 0.6666666666666666 t) (+ a (/ 5.0 6.0))))
6.0ms	(/ (sqrt (+ t a)) t)
10.0ms	(* z (/ (sqrt (+ t a)) t))
15.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 0.6666666666666666 t) (+ a (/ 5.0 6.0)))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (- b c) (- (/ 0.6666666666666666 t) (+ a (/ 5.0 6.0))))
12.0ms	(/ (sqrt (+ t a)) t)
17.0ms	(* z (/ (sqrt (+ t a)) t))
55.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 0.6666666666666666 t) (+ a (/ 5.0 6.0)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5645	3349

prune316.0ms

Filtered

121 candidates to 169 candidates (-39.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	170	4	174

Merged error: 0.3b

Counts

174 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* t 3.0))
1.1b	(* z (/ (sqrt (+ t a)) t))
3.3b	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (log (exp (/ 2.0 (* t 3.0)))) (+ a (/ 5.0 6.0)))))
4.1b	(log (exp (/ 2.0 (* t 3.0))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
29×	`times-frac`
26×	`add-cube-cbrt`
25×	`associate-r`
14×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
11×	`associate-*r/`
9×	`log-prod`
8×	`associate-+r+` `frac-add` `log-pow`
7×	`pow1` `exp-prod`
6×	`flip3--` `associate--l+` `flip--` `add-log-exp`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in`
3×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `associate-/l*` `unswap-sqr`
2×	`sub-neg` `associate-*l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `rem-log-exp` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `flip-+`

Counts

4 → 112

Calls

4 calls:

4.0ms	(/ 2.0 (* t 3.0))
10.0ms	(* z (/ (sqrt (+ t a)) t))
14.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (log (exp (/ 2.0 (* t 3.0)))) (+ a (/ 5.0 6.0)))))
4.0ms	(log (exp (/ 2.0 (* t 3.0))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 2.0 (* t 3.0))
17.0ms	(* z (/ (sqrt (+ t a)) t))
55.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (log (exp (/ 2.0 (* t 3.0)))) (+ a (/ 5.0 6.0)))))
2.0ms	(log (exp (/ 2.0 (* t 3.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5045	1947

prune265.0ms

Filtered

93 candidates to 124 candidates (-33.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	124	4	128

Merged error: 0.3b

Counts

128 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ t a)) t)
0.7b	(- (* c (+ a 0.8333333333333334)) (* a b))
1.1b	(* z (/ (sqrt (+ t a)) t))
2.4b	(+ (* z (/ (sqrt (+ t a)) t)) (- (* c (+ a 0.8333333333333334)) (* a b)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
44×	`times-frac`
43×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
29×	`sqrt-prod`
25×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out` `associate-/l*`
6×	`pow1`
4×	`associate--l+`
3×	`associate-+r+` `associate-r/` `associate-l` `associate-/r` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `sqrt-div` `diff-log` `div-exp` `frac-add` `prod-exp` `sum-log` `flip--` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 121

Calls

4 calls:

12.0ms	(/ (sqrt (+ t a)) t)
11.0ms	(- (* c (+ a 0.8333333333333334)) (* a b))
19.0ms	(* z (/ (sqrt (+ t a)) t))
14.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (- (* c (+ a 0.8333333333333334)) (* a b)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (sqrt (+ t a)) t)
8.0ms	(- (* c (+ a 0.8333333333333334)) (* a b))
17.0ms	(* z (/ (sqrt (+ t a)) t))
35.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (- (* c (+ a 0.8333333333333334)) (* a b)))

simplify33.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5096	1752

prune173.0ms

Filtered

91 candidates to 133 candidates (-46.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	133	4	137

Merged error: 0.3b

Counts

137 → 4

regimes841.0ms

Accuracy

62.3% (3.5b remaining)

Error of 4.1b against oracle of 0.5b and baseline of 9.9b

bsearch200.0ms

Steps

Iters	Range		Point
9	4.808173090191861e-12	0.0008815761181209453	0.000868470817534886
8	-7.017868864164815e-303	-8.357826202093129e-306	-4.595287319339345e-303
7	-1.0729206312326081e-265	-6.591963202372316e-267	-2.683950136323593e-266
6	-3.02582738990408e-113	-3.232129934162935e-114	-1.6844335713955825e-113

simplify26.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	1023	227
1	1023	227

end0.0ms

sample1.9s

Algorithm

intervals

Results

810.0ms	8000×	body	80	valid
501.0ms	5111×	body	80	nan

Details

analyze1.8s

sample63.0ms

simplify29.0ms

prune23.0ms

localize25.0ms

rewrite39.0ms

series81.0ms

simplify56.0ms

prune297.0ms

localize24.0ms

rewrite58.0ms

series98.0ms

simplify48.0ms

prune316.0ms

localize31.0ms

rewrite37.0ms

series76.0ms

simplify36.0ms

prune265.0ms

localize21.0ms

rewrite68.0ms

series72.0ms

simplify33.0ms

prune173.0ms

regimes841.0ms

bsearch200.0ms

simplify26.0ms

end0.0ms

sample1.9s

Profiling