Details

sample87.0ms

Algorithm

intervals

Results

13.0ms	185×	body	80	valid
13.0ms	142×	body	80	nan
9.0ms	28×	body	1280	nan
8.0ms	33×	body	640	nan
8.0ms	24×	body	1280	valid
6.0ms	25×	body	640	valid
3.0ms	15×	body	320	nan
2.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	9×	body	160	nan

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune4.0ms

Filtered

1 candidates to 0 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: 40.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
8.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

16.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
12.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
56.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
184.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify58.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune208.0ms

Filtered

92 candidates to 65 candidates (29.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Merged error: 2.8b

Counts

93 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
1.0b	(pow (sqrt 2.0) 3)
11.3b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
11.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`div-exp`
13×	`prod-exp`
10×	`sqrt-prod`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`unpow-prod-down` `times-frac` `cube-prod` `associate-l` `associate-/l*`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `*-commutative` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
3.0ms	(pow (sqrt 2.0) 3)
10.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
6.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series29.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
0.0ms	(pow (sqrt 2.0) 3)
16.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
9.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify76.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	379	567
1	2149	506
2	5002	498

prune281.0ms

Filtered

116 candidates to 61 candidates (47.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	112	8	120

Merged error: 2.8b

Counts

120 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
1.0b	(pow (sqrt 2.0) 3)
11.3b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
11.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`div-exp`
13×	`prod-exp`
10×	`sqrt-prod`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`unpow-prod-down` `times-frac` `cube-prod` `associate-l` `associate-/l*`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `*-commutative` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
3.0ms	(pow (sqrt 2.0) 3)
10.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
6.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series29.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
0.0ms	(pow (sqrt 2.0) 3)
16.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
9.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify70.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	355	548
1	1993	487
2	5003	479

prune369.0ms

Filtered

116 candidates to 61 candidates (47.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	116	8	124

Merged error: 2.8b

Counts

124 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
1.0b	(pow (sqrt 2.0) 3)
11.3b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
11.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
12×	`prod-exp`
8×	`pow-to-exp` `pow-exp`
6×	`pow1` `unpow-prod-down` `times-frac` `cube-prod` `sqrt-prod` `associate-/l*`
4×	`cbrt-undiv` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `pow-pow`
2×	`frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `pow1/3` `unpow3` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 95

Calls

4 calls:

1.0ms	(cbrt t)
3.0ms	(pow (sqrt 2.0) 3)
8.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
6.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series51.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(cbrt t)
0.0ms	(pow (sqrt 2.0) 3)
16.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
9.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	367	517
1	1740	455
2	5001	441

prune302.0ms

Filtered

105 candidates to 57 candidates (45.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	104	9	113

Merged error: 2.8b

Counts

113 → 9

regimes614.0ms

Accuracy

74.5% (5.8b remaining)

Error of 10.8b against oracle of 4.9b and baseline of 27.9b

bsearch141.0ms

Steps

Iters	Range		Point
10	2.074769226712566e-208	2.172012608900755e-196	1.1213056196597745e-200
6	-0.3446774858643339	-0.029868786149610006	-0.33790579127472004

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	57
1	59	57

end0.0ms

sample2.3s

Algorithm

intervals

Results

386.0ms	5568×	body	80	valid
272.0ms	854×	body	1280	nan
246.0ms	3811×	body	80	nan
224.0ms	702×	body	1280	valid
222.0ms	880×	body	640	valid
211.0ms	863×	body	640	nan
100.0ms	538×	body	320	valid
87.0ms	479×	body	320	nan
40.0ms	312×	body	160	valid
36.0ms	273×	body	160	nan

Details

sample87.0ms

simplify81.0ms

prune4.0ms

localize16.0ms

rewrite50.0ms

series331.0ms

simplify58.0ms

prune208.0ms

localize23.0ms

rewrite27.0ms

series29.0ms

simplify76.0ms

prune281.0ms

localize28.0ms

rewrite27.0ms

series29.0ms

simplify70.0ms

prune369.0ms

localize36.0ms

rewrite21.0ms

series51.0ms

simplify54.0ms

prune302.0ms

regimes614.0ms

bsearch141.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling