Details

sample56.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
17.0ms	237×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune444.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
32×	`add-cube-cbrt`
31×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 130

Calls

4 calls:

14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
4.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
149.0ms	(* (log base) (log base))
150.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	386	1610
1	1345	1484
2	5002	1464

prune642.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	146	478
1	405	458
2	1153	456
3	5001	452

prune406.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
22×	`pow1`
19×	`associate-l`
18×	`log-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
12×	`add-exp-log` `associate--l+`
11×	`add-cbrt-cube`
10×	`times-frac`
8×	`associate-r`
7×	`log-pow`
6×	`swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `sub-neg` `flip3--` `flip3-+` `sqrt-div` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `flip--` `flip-+`
1×	`cbrt-undiv` `pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `associate-*l/` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv` `difference-of-squares` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

56.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
1.0ms	(pow (log base) 4)
3.0ms	(sqrt (+ (* re re) (* im im)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))
164.0ms	(pow (log base) 4)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	662	2168
1	3246	1970
2	5002	1964

prune497.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.4b

regimes397.0ms

Accuracy

55.9% (11.0b remaining)

Error of 17.9b against oracle of 6.9b and baseline of 31.8b

bsearch104.0ms

Steps

Iters	Range		Point
4	3.0132129284976687e+58	4.410176380362178e+58	4.3665212724914114e+58
7	-9.152284158066109e+123	-1.950434751003955e+122	-2.4957556616996032e+123

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	55
1	53	55

end0.0ms

sample1.5s

Algorithm

intervals

Results

591.0ms	8140×	body	80	nan
569.0ms	8000×	body	80	valid