Details

sample75.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
23.0ms	251×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 33.7b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))
31.1b	(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:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (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)))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4927	2020
1	4927	2020

prune243.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 10.1b

Counts

123 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
41.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
16.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify37.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5446	1936

prune231.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	101	17	118

Merged error: 10.0b

Counts

118 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5007	593

prune185.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	76	17	93

Merged error: 10.0b

Counts

93 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod`
11×	`log-pow`
10×	`associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
17.0ms	(pow (log base) 4)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5002	940

prune147.0ms

Filtered

65 candidates to 109 candidates (-67.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	109	17	126

Merged error: 10.0b

Counts

126 → 17

regimes587.0ms

Accuracy

58.2% (10.2b remaining)

Error of 17.6b against oracle of 7.4b and baseline of 31.8b

bsearch54.0ms

Steps

Iters	Range		Point
1	1130.7758405393088	1253.8160530937032	1223.0559999551044
9	-2.170247441352149e+133	-2.471576061565681e+124	-1.0229096307000107e+130

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	75
1	46	75

end0.0ms

sample2.0s

Algorithm

intervals

Results

759.0ms	8000×	body	80	valid
702.0ms	7791×	body	80	nan

Details

sample75.0ms

simplify3.0ms

prune4.0ms

localize18.0ms

rewrite26.0ms

series66.0ms

simplify84.0ms

prune243.0ms

localize21.0ms

rewrite23.0ms

series83.0ms

simplify37.0ms

prune231.0ms

localize28.0ms

rewrite15.0ms

series31.0ms

simplify37.0ms

prune185.0ms

localize27.0ms

rewrite19.0ms

series57.0ms

simplify48.0ms

prune147.0ms

regimes587.0ms

bsearch54.0ms

simplify1.0ms

end0.0ms

sample2.0s

Profiling