Details

sample66.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
20.0ms	246×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

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:

34.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
85.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
145.0ms	(* (log base) (log base))
32.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune923.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
0.5b	(* (log base) (log base))
28.7b	(sqrt (+ (* re re) (* im im)))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
58×	`add-sqr-sqrt`
42×	`pow1`
34×	`sqrt-pow1`
28×	`sqrt-div`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`swap-sqr`
18×	`pow1/2`
13×	`associate-r` `associate-l`
10×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
6×	`log-prod` `pow-prod-down` `pow-sqr` `log-pow`
4×	`frac-times` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`pow2` `rem-sqrt-square` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sqrt-unprod` `rem-square-sqrt`

Counts

4 → 149

Calls

4 calls:

52.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
338.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	299	1042
1	1157	957
2	5002	925

prune946.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
28.7b	(sqrt (+ (* re re) (* im im)))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
9.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt base)
176.0ms	(cbrt base)
32.0ms	(sqrt (+ (* re re) (* im im)))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	124	278
1	290	266
2	689	262
3	1947	262
4	5002	262

prune882.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
44.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
3.0ms	(pow (log base) 2)
11.0ms	(sqrt (+ (* re re) (* im im)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
129.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
149.0ms	(pow (log base) 2)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	443	1231
1	1594	1134
2	5002	1115

prune722.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.1b

regimes646.0ms

Accuracy

60.3% (9.8b remaining)

Error of 17.0b against oracle of 7.2b and baseline of 31.9b

bsearch241.0ms

Steps

Iters	Range		Point
6	1.1049349221518308e+122	5.264316198201932e+122	2.1006760882161104e+122
8	-1.7085646837476792e+140	-2.501669300968147e+136	-3.12098675750462e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	48
1	62	48

end0.0ms

sample1.8s

Algorithm

intervals

Results

742.0ms	8000×	body	80	valid
670.0ms	8038×	body	80	nan