Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	250×	body	80	nan
17.0ms	256×	body	80	valid

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: 34.0b

localize23.0ms

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))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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))
9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
96.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))
35.0ms	(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

prune456.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.1b

localize27.0ms

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))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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:

11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
145.0ms	(* (log base) (log base))
146.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (37.0ms)

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

prune537.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (* (log base) (log base)) (* (log base) (log base)))
0.7b	(pow (* (log base) (log base)) 3)
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

137×	`pow1`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
21×	`add-exp-log` `add-cbrt-cube`
20×	`pow-plus`
19×	`add-sqr-sqrt`
18×	`log-prod` `*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`pow2` `distribute-rgt-in` `distribute-lft-in`
10×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr`
6×	`pow-pow` `log-pow`
5×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-div` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `cube-prod` `flip-+` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

5.0ms	(* (log base) (log base))
11.0ms	(* (* (log base) (log base)) (* (log base) (log base)))
5.0ms	(pow (* (log base) (log base)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (log base) (log base))
308.0ms	(* (* (log base) (log base)) (* (log base) (log base)))
189.0ms	(pow (* (log base) (log base)) 3)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	407	550
1	1667	500
2	5002	477

prune649.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 9.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
173.0ms	(cbrt base)
181.0ms	(cbrt base)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	366	1306
1	1283	1187
2	5001	1169

prune398.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 9.6b

regimes655.0ms

Accuracy

56.2% (10.9b remaining)

Error of 17.9b against oracle of 7.0b and baseline of 31.9b

bsearch191.0ms

Steps

Iters	Range		Point
7	1.226560857263168e+30	3.8140867878192627e+31	3.6965442466504777e+31
10	-1.6626715053611692e+123	-7.69960824793385e+108	-8.682521958621949e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	64
1	67	64

end0.0ms

sample1.4s

Algorithm

intervals

Results

540.0ms	7787×	body	80	nan
535.0ms	8000×	body	80	valid