Details

analyze1.7s

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

sample69.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
17.0ms	187×	body	80	nan

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5545	33

prune21.0ms

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: 2.5b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ t a)) t)
0.3b	(/ 2.0 (* t 3.0))
1.1b	(* z (/ (sqrt (+ t a)) t))
2.3b	(+ (* 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))
10.0ms	(* z (/ (sqrt (+ t a)) t))
13.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))

series80.0ms

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))
51.0ms	(+ (* z (/ (sqrt (+ t a)) t)) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4991	2716
1	4991	2716

prune277.0ms

Filtered

106 candidates to 150 candidates (-41.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	149	3	152

Merged error: 0.2b

Counts

152 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x (* y (pow (exp 2.0) (- (* c (+ a 0.8333333333333334)) (* a b))))))
0.0b	(* y (pow (exp 2.0) (- (* c (+ a 0.8333333333333334)) (* a b))))
0.0b	(* c (+ a 0.8333333333333334))
0.7b	(- (* c (+ a 0.8333333333333334)) (* a b))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`associate-r`
12×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-l` `add-log-exp`
4×	`unpow-prod-down` `prod-exp` `associate--l+` `unswap-sqr`
3×	`unpow-prod-up` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-/r` `associate-/l*`
2×	`sub-neg` `flip3-+` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out` `pow-sub`

Counts

4 → 94

Calls

4 calls:

5.0ms	(/ x (+ x (* y (pow (exp 2.0) (- (* c (+ a 0.8333333333333334)) (* a b))))))
6.0ms	(* y (pow (exp 2.0) (- (* c (+ a 0.8333333333333334)) (* a b))))
6.0ms	(* c (+ a 0.8333333333333334))
6.0ms	(- (* c (+ a 0.8333333333333334)) (* a b))

series90.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ x (+ x (* y (pow (exp 2.0) (- (* c (+ a 0.8333333333333334)) (* a b))))))
29.0ms	(* y (pow (exp 2.0) (- (* c (+ a 0.8333333333333334)) (* a b))))
5.0ms	(* c (+ a 0.8333333333333334))
8.0ms	(- (* c (+ a 0.8333333333333334)) (* a b))

simplify67.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4994	1622
1	4994	1622

prune180.0ms

Filtered

80 candidates to 106 candidates (-32.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	106	3	109

Merged error: 0.2b

Counts

109 → 3

localize36.0ms

Local error

Found 4 expressions with local error:

3.1b	(* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))))))
6.6b	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
7.5b	(+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0)))))))))
28.9b	(/ (+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))))))) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

1962×	`associate-*r/`
498×	`flip3--` `flip--`
368×	`frac-times`
320×	`frac-add`
246×	`sqrt-div`
204×	`frac-sub`
162×	`associate-/l/`
125×	`flip3-+` `flip-+`
116×	`associate-*l/`
96×	`distribute-rgt-in` `distribute-lft-in`
56×	`sub-neg`
37×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-+l+` `associate--l+`
13×	`pow-prod-down`
12×	`associate-+r+`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv`

Counts

4 → 486

Calls

4 calls:

24.0ms	(* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))))))
18.0ms	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
32.0ms	(+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0)))))))))
52.0ms	(/ (+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))))))) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))))))
22.0ms	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
170.0ms	(+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0)))))))))
252.0ms	(/ (+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) (* t (* (- b c) (- (* 2.0 (- a (/ 5.0 6.0))) (* t (* 3.0 (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))))))))) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

simplify260.0ms

Algorithm

egg-herbie

Counts

498 → 498

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4998	43729
1	4998	43729

prune10.1s

Filtered

447 candidates to 498 candidates (-11.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	497	1	498
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	497	4	501

Merged error: 0b

Counts

501 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* t (* t (* 3.0 (- a (/ 5.0 6.0)))))
0.2b	(* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))
6.6b	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
30.3b	(/ (+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) 0) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

56×	`distribute-rgt-in` `distribute-lft-in`
50×	`add-exp-log` `add-cbrt-cube`
48×	`associate-*r/`
36×	`pow1`
32×	`sub-neg`
28×	`prod-exp` `cbrt-unprod`
22×	`pow-prod-down`
13×	`associate-l`
12×	`*-un-lft-identity` `sqrt-div`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`frac-times` `flip3--` `flip--`
7×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `sqrt-prod` `add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 149

Calls

4 calls:

13.0ms	(* t (* t (* 3.0 (- a (/ 5.0 6.0)))))
16.0ms	(* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))
19.0ms	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
35.0ms	(/ (+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) 0) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* t (* t (* 3.0 (- a (/ 5.0 6.0)))))
17.0ms	(* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))
24.0ms	(* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0))))))
81.0ms	(/ (+ (* z (* (sqrt (+ t a)) (* t (* 3.0 (- a (/ 5.0 6.0)))))) 0) (* t (* t (* 3.0 (- a (/ 5.0 6.0))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4923	3068
1	4923	3068

prune236.0ms

Filtered

89 candidates to 161 candidates (-80.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	161	4	165

Merged error: 0b

Counts

165 → 4

regimes694.0ms

Accuracy

-8.7% (3.3b remaining)

Error of 3.5b against oracle of 0.3b and baseline of 3.3b

bsearch140.0ms

Steps

Iters	Range		Point
7	1.0347651448899267e-105	1.4983494932274888e-103	1.0591402684185584e-105
9	-5.08690992619926e-08	-8.39211256095451e-14	-1.9720158333783228e-13

simplify22.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	915	109
1	915	109

end0.0ms

sample2.0s

Algorithm

intervals

Results

821.0ms	8000×	body	80	valid
673.0ms	4909×	body	80	nan

Details

analyze1.7s

sample69.0ms

simplify30.0ms

prune21.0ms

localize24.0ms

rewrite39.0ms

series80.0ms

simplify58.0ms

prune277.0ms

localize17.0ms

rewrite25.0ms

series90.0ms

simplify67.0ms

prune180.0ms

localize36.0ms

rewrite213.0ms

series489.0ms

simplify260.0ms

prune10.1s

localize25.0ms

rewrite92.0ms

series128.0ms

simplify62.0ms

prune236.0ms

regimes694.0ms

bsearch140.0ms

simplify22.0ms

end0.0ms

sample2.0s

Profiling