Details

sample76.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
23.0ms	257×	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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.6b

Counts

2 → 1

localize26.0ms

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))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
107.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
169.0ms	(* (log base) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5002	1203

prune751.0ms

Filtered

122 candidates to 84 candidates (31.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 6.7b

Counts

123 → 15

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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:

4.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
47.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(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

prune801.0ms

Filtered

73 candidates to 61 candidates (16.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	73	15	88

Merged error: 6.7b

Counts

88 → 15

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (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))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 174

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (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)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
168.0ms	(* (log base) (log base))
168.0ms	(* (log base) (log base))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	676	3305
1	3766	2940
2	5001	2757

prune966.0ms

Filtered

186 candidates to 103 candidates (44.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	184	17	201

Merged error: 6.6b

Counts

201 → 17

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (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)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

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:

18.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (pow (log base) 4))) (- (* (log base) (log base)) (* 0.0 0.0)))
172.0ms	(* (log base) (log base))
190.0ms	(pow (log base) 4)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	662	2168
1	3246	1970
2	5001	1964

prune959.0ms

Filtered

136 candidates to 83 candidates (39.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	3	12	15
Picked	1	0	1
Done	0	1	1
Total	135	18	153

Merged error: 6.6b

Counts

153 → 18

regimes836.0ms

Accuracy

56.3% (10.6b remaining)

Error of 18.1b against oracle of 7.6b and baseline of 31.7b

bsearch241.0ms

Steps

Iters	Range		Point
3	1.271206889782828e+124	1.59796910122065e+124	1.4550106337166028e+124
1	3.2435519224687896e-248	3.3776482887491227e-248	3.3441241971790394e-248
7	-2.182942072178726e-246	-1.163006954732957e-247	-1.972444937254012e-246
10	-6.009142246337554e+160	-4.091974005961926e+146	-2.4647497111965144e+148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	97
1	67	97

end0.0ms

sample2.0s

Algorithm

intervals

Results

734.0ms	8000×	body	80	valid
681.0ms	7848×	body	80	nan

Details

sample76.0ms

simplify4.0ms

prune6.0ms

localize26.0ms

rewrite27.0ms

series434.0ms

simplify64.0ms

prune751.0ms

localize28.0ms

rewrite17.0ms

series245.0ms

simplify44.0ms

prune801.0ms

localize28.0ms

rewrite47.0ms

series539.0ms

simplify101.0ms

prune966.0ms

localize32.0ms

rewrite33.0ms

series528.0ms

simplify94.0ms

prune959.0ms

regimes836.0ms

bsearch241.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling