Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

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: 27.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
27.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

198×	`*-un-lft-identity`
80×	`distribute-lft-out`
75×	`associate-l`
56×	`times-frac`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
16×	`swap-sqr`
12×	`fma-def`
8×	`associate-/r*`
7×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `*-commutative` `div-inv` `unswap-sqr`

Counts

2 → 118

Calls

2 calls:

13.0ms	(+ (* a c) (* b d))
35.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* a c) (* b d))
89.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify106.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	243	976
1	848	880
2	3077	858
3	5001	858

prune157.0ms

Filtered

124 candidates to 55 candidates (55.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 17.8b

Counts

125 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot c d) 1))
0.3b	(fma a c (* b d))
0.3b	(* (/ 1 (/ (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
17.4b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

571×	`add-sqr-sqrt`
552×	`associate-/r*`
463×	`times-frac`
431×	`*-un-lft-identity`
374×	`add-cube-cbrt`
361×	`frac-times`
170×	`add-exp-log`
138×	`associate-/l*`
133×	`associate-l`
124×	`associate-r`
102×	`unswap-sqr`
93×	`div-exp`
62×	`prod-exp`
50×	`add-cbrt-cube`
46×	`clear-num`
44×	`frac-2neg`
41×	`1-exp`
31×	`div-inv`
28×	`*-commutative`
22×	`associate-/r/`
20×	`cbrt-undiv`
19×	`associate-r/` `associate-l/`
15×	`rec-exp`
13×	`cbrt-unprod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`un-div-inv` `remove-double-div`
1×	`pow-flip` `pow-prod-down` `fma-udef` `inv-pow`

Counts

4 → 761

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot c d) 1))
1.0ms	(fma a c (* b d))
62.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
7.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series427.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1 (/ (hypot c d) 1))
45.0ms	(fma a c (* b d))
198.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
123.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify152.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	3091	8405
1	5001	7374

prune999.0ms

Filtered

773 candidates to 281 candidates (63.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	764	9	773
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	774	9	783

Merged error: 5.9b

Counts

783 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (/ (/ (hypot c d) 1) (sqrt 1)))
0.3b	(fma a c (* b d))
17.4b	(/ (fma a c (* b d)) (hypot c d))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

3679×	`times-frac`
1571×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
549×	`sqrt-prod`
184×	`div-inv`
97×	`associate-/r*`
35×	`associate-/l*`
33×	`add-exp-log`
31×	`associate-/r/`
26×	`add-cbrt-cube`
23×	`div-exp`
18×	`associate-/l/`
16×	`cbrt-undiv`
5×	`frac-2neg` `clear-num`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`1-exp`
1×	`fma-udef`

Counts

3 → 1266

Calls

3 calls:

42.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (/ (/ (hypot c d) 1) (sqrt 1)))
1.0ms	(fma a c (* b d))
3.0ms	(/ (fma a c (* b d)) (hypot c d))

series284.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (/ (/ (hypot c d) 1) (sqrt 1)))
39.0ms	(fma a c (* b d))
120.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify282.0ms

Algorithm

egg-herbie

Counts

1275 → 1275

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	26953

prune2.9s

Filtered

1275 candidates to 788 candidates (38.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1270	5	1275
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	1275	9	1284

Merged error: 5.8b

Counts

1284 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (/ (/ (hypot c d) 1) (sqrt 1)))
0.3b	(fma a c (* b d))
7.4b	(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
10.1b	(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

49459×	`times-frac`
19850×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15468×	`sqrt-prod`
1552×	`div-inv`
205×	`associate-/l*`
121×	`associate-/r*`
76×	`associate-/l/`
59×	`add-exp-log`
47×	`add-cbrt-cube`
43×	`div-exp`
31×	`cbrt-undiv` `associate-/r/`
8×	`frac-2neg` `clear-num`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`1-exp`
1×	`fma-udef`

Counts

4 → 11716

Calls

4 calls:

284.0ms	(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (/ (/ (hypot c d) 1) (sqrt 1)))
1.0ms	(fma a c (* b d))
12.0ms	(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
8.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (/ (/ (hypot c d) 1) (sqrt 1)))
43.0ms	(fma a c (* b d))
119.0ms	(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
210.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify3.9s

Algorithm

egg-herbie

Counts

11728 → 11728

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	10539	407730

prune33.1s

Filtered

11728 candidates to 6211 candidates (47.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	11725	3	11728
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	11726	11	11737

Merged error: 5.1b

Counts

11737 → 11

regimes226.0ms

Accuracy

33.8% (7.8b remaining)

Error of 13.3b against oracle of 5.6b and baseline of 17.3b

bsearch70.0ms

Steps

Iters	Range		Point
7	1.967467882740907e+106	7.856463001522747e+107	1.2363859313436468e+107
6	-6.52330204454965e+152	-1.537752741313912e+152	-1.999293010764536e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	20
1	29	20
2	29	20

end0.0ms

sample512.0ms

Algorithm

intervals

Results

303.0ms

8440×

body

valid