Details

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	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: 34.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* re re) (* im im))
126.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	256	741
1	895	697
2	2846	694
3	5001	694

prune221.0ms

Filtered

83 candidates to 55 candidates (66.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	12	84

Merged error: 5.9b

Counts

84 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt` `log-pow`
53×	`pow1`
46×	`associate-r`
28×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`flip3-+` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`+-commutative` `frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 205

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
31.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
8.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
135.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
205.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	648	2798
1	2878	2493
2	5002	2395

prune471.0ms

Filtered

217 candidates to 110 candidates (50.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	204	13	217
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	211	18	229

Merged error: 5.7b

Counts

229 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
46×	`times-frac`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
38×	`sqrt-prod`
25×	`pow-unpow` `associate-l`
20×	`log-prod`
18×	`unpow-prod-down`
15×	`pow1`
14×	`add-exp-log`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
7×	`log-pow`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`associate-r` `prod-exp`
3×	`pow-pow` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `sum-log` `-commutative` `sqrt-pow2`

Counts

4 → 141

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
18.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* re re) (* im im))
351.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
338.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	593	2050
1	2744	1681
2	5001	1554

prune430.0ms

Filtered

153 candidates to 92 candidates (60.1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	146	7	153
Fresh	5	12	17
Picked	0	1	1
Done	0	0	0
Total	151	20	171

Merged error: 5.7b

Counts

171 → 20

localize25.0ms

Local error

Found 4 expressions with local error:

3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.4b	(sqrt (+ (* re re) (* im im)))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow-unpow`
42×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqrt-prod`
16×	`pow1`
12×	`unpow-prod-down`
6×	`add-exp-log` `pow-pow` `log-pow`
4×	`sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `flip3-+` `pow-exp` `sqrt-pow2` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
340.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	305	1184
1	1001	1106
2	3338	1032
3	5001	1028

prune560.0ms

Filtered

132 candidates to 86 candidates (65.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	3	15	18
Picked	1	0	1
Done	1	0	1
Total	135	17	152

Merged error: 5.7b

Counts

152 → 17

regimes863.0ms

Accuracy

56% (10.9b remaining)

Error of 18.5b against oracle of 7.5b and baseline of 32.4b

bsearch379.0ms

Steps

Iters	Range		Point
7	1.1965702813225714e+120	7.306927196198172e+121	8.040497153778162e+120
10	3.3746055148489886e-168	6.644118788358932e-151	1.582163645573821e-167
7	2.363660519479911e-304	1.3429956514040144e-302	2.5518471897600652e-303
10	-2.5170109662579546e-211	-5.785550335923721e-221	-5.916003073595471e-212
10	-2.368742889503448e-151	-4.8620484299604695e-170	-4.942878981580837e-156
10	-1.930778967641709e+126	-1.7976808176493555e+110	-3.0511758492970502e+113

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	165
1	89	165
2	89	165

end0.0ms

sample495.0ms

Algorithm

intervals

Results

356.0ms

8000×

body

valid