Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

271×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Filtered

1 candidates to 0 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: 27.8b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
27.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series128.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ (* a c) (* b d))
87.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify82.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412

prune127.0ms

Filtered

48 candidates to 38 candidates (79.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	8	49

Merged error: 27.0b

Counts

49 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
17.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

19.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
9.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
107.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify91.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	714	5680
1	2516	5201
2	5001	5144

prune482.0ms

Filtered

276 candidates to 143 candidates (51.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	272	4	276
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	274	10	284

Merged error: 24.3b

Counts

284 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
17.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

24.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
12.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
109.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify80.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	567	2505
1	3282	2242
2	5001	2117

prune363.0ms

Filtered

172 candidates to 113 candidates (65.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	172	10	182

Merged error: 24.3b

Counts

182 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a c) (* b d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
27.0b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 126

Calls

3 calls:

3.0ms	(+ (* a c) (* b d))
9.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
8.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* a c) (* b d))
135.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
55.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify63.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	480	1744
1	2237	1592
2	5003	1505

prune200.0ms

Filtered

135 candidates to 75 candidates (55.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	135	10	145

Merged error: 24.3b

Counts

145 → 10

regimes150.0ms

Accuracy

5.5% (2.7b remaining)

Error of 25.6b against oracle of 22.9b and baseline of 25.8b

bsearch38.0ms

Steps

Iters	Range		Point
7	7.224436801969521e+81	4.463973393884511e+83	1.6167157221602814e+83

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	19
1	26	19

end0.0ms

sample509.0ms

Algorithm

intervals

Results

291.0ms

8443×

body

valid