Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

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))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

2.0ms	(+ (* re re) (* im im))
11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
128.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

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

prune211.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
30.4b	(log (+ (* re re) (* im im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
83×	`add-sqr-sqrt`
54×	`sqrt-prod`
53×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
19×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`div-sub`
1×	`+-commutative` `frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 164

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
31.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
9.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
3.0ms	(log (+ (* re re) (* im im)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* re re) (* im im))
133.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
175.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
45.0ms	(log (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	563	2159
1	2395	1981
2	5002	1899

prune391.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
13.0b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
18.3b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`times-frac`
40×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
13×	`pow1`
12×	`add-exp-log` `unpow-prod-down`
9×	`add-cbrt-cube`
8×	`log-pow`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-log-exp`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-pow` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
24.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
5.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
6.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
387.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
283.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
439.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	554	1776
1	2519	1567
2	5002	1445

prune371.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
30.4b	(log (+ (* re re) (* im im)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
131×	`add-sqr-sqrt`
107×	`sqrt-prod`
79×	`add-cube-cbrt` `*-un-lft-identity`
78×	`add-exp-log`
68×	`associate-l`
59×	`add-cbrt-cube`
42×	`pow1`
33×	`associate-r`
31×	`prod-exp` `log-pow`
27×	`div-exp`
22×	`cbrt-unprod`
18×	`cbrt-undiv`
15×	`unswap-sqr`
7×	`associate-/r*`
6×	`frac-times` `associate-*r/`
5×	`1-exp`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`log-prod`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`frac-2neg` `rem-log-exp` `clear-num`

Counts

4 → 245

Calls

4 calls:

47.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
43.0ms	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
10.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
3.0ms	(log (+ (* re re) (* im im)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
218.0ms	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
183.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
52.0ms	(log (+ (* re re) (* im im)))

simplify119.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	888	3877
1	4541	3356
2	5001	3222

prune578.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 6.5b

regimes497.0ms

Accuracy

56.1% (11.1b remaining)

Error of 17.9b against oracle of 6.8b and baseline of 32.0b

bsearch108.0ms

Steps

Iters	Range		Point
10	7.491092794297452e+92	1.1133938054187134e+105	2.4086845449201843e+100
10	-5.991532222681368e+46	-9.78963830731076e+36	-5.629472522245536e+46

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	38
1	50	38

end0.0ms

sample489.0ms

Algorithm

intervals

Results

351.0ms

8000×

body

valid