Details

sample66.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
19.0ms	223×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

prune4.0ms

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: 32.1b

Counts

2 → 1

localize24.0ms

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))
29.7b	(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:

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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
23.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4927	2020
1	4927	2020

prune261.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	17	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	17	123

Merged error: 6.9b

Counts

123 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `log-prod` `associate-l` `log-pow` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(pow (log base) 2)
14.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4943	828
1	4943	828

prune235.0ms

Filtered

58 candidates to 93 candidates (-60.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	90	20	110

Merged error: 6.8b

Counts

110 → 20

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4)))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
45×	`times-frac`
44×	`unpow-prod-down`
36×	`difference-of-squares`
33×	`add-cube-cbrt`
25×	`sqr-pow`
24×	`pow1`
15×	`associate-/r*`
12×	`distribute-lft-out--`
11×	`log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-prod` `swap-sqr`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow2` `pow-to-exp` `rem-sqrt-square` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

16.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4)))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4)))
14.0ms	(* (log base) (log base))
17.0ms	(pow (log base) 4)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5030	3969

prune332.0ms

Filtered

94 candidates to 160 candidates (-70.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	4	14	18
Picked	1	0	1
Done	0	1	1
Total	158	22	180

Merged error: 6.8b

Counts

180 → 22

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `sqrt-div` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow1/3` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `flip-+` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

4.0ms	(* (log base) (log base))
2.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
5.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (log base) (log base))
23.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
48.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4933	983
1	4933	983

prune125.0ms

Filtered

65 candidates to 102 candidates (-56.9%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	1	19	20
Picked	0	1	1
Done	0	1	1
Total	98	26	124

Merged error: 6.8b

Counts

124 → 26

regimes845.0ms

Accuracy

56.3% (10.8b remaining)

Error of 18.2b against oracle of 7.4b and baseline of 32.2b

bsearch177.0ms

Steps

Iters	Range		Point
7	4.7114067075677415e+112	3.978630942929399e+114	2.0832334970782824e+114
9	4.1760177309814186e-137	3.6476347041017933e-131	4.217323438882182e-137
6	3.877833218120514e-227	2.413185294496458e-226	1.9687026774711904e-226
9	-2.153916927257551e+110	-6.281241613755338e+103	-1.6904894801732315e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	156
1	62	156

end0.0ms

sample2.0s

Algorithm

intervals

Results

748.0ms	8000×	body	80	valid
718.0ms	8126×	body	80	nan

Details

sample66.0ms

simplify3.0ms

prune4.0ms

localize24.0ms

rewrite27.0ms

series68.0ms

simplify85.0ms

prune261.0ms

localize24.0ms

rewrite15.0ms

series56.0ms

simplify58.0ms

prune235.0ms

localize25.0ms

rewrite33.0ms

series70.0ms

simplify92.0ms

prune332.0ms

localize26.0ms

rewrite17.0ms

series91.0ms

simplify46.0ms

prune125.0ms

regimes845.0ms

bsearch177.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling