Details

sample80.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
24.0ms	244×	body	80	nan

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

prune5.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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:

7.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
27.0ms	(/ (+ (* (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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4919	2020
1	4919	2020

prune263.0ms

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: 6.9b

Counts

123 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

33.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
5.0ms	(sqrt (+ (* re re) (* im im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
16.0ms	(pow (log base) 2)
16.0ms	(pow (log base) 2)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4974	4109
1	4974	4109

prune396.0ms

Filtered

88 candidates to 152 candidates (-72.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	149	16	165

Merged error: 6.9b

Counts

165 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`pow1` `cbrt-prod` `unpow-prod-down`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-div` `associate-/r/` `log-pow` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
2.0ms	(cbrt (pow (log base) 6))
3.0ms	(pow (log base) 6)
5.0ms	(sqrt (+ (* re re) (* im im)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
16.0ms	(cbrt (pow (log base) 6))
23.0ms	(pow (log base) 6)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5109	1566

prune225.0ms

Filtered

62 candidates to 92 candidates (-48.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	91	17	108

Merged error: 6.9b

Counts

108 → 17

localize23.0ms

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)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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:

7.0ms	(* (log base) (log base))
2.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
6.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
5.0ms	(sqrt (+ (* re re) (* im im)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (log base) (log base))
24.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
57.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4897	983
1	4897	983

prune142.0ms

Filtered

65 candidates to 102 candidates (-56.9%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	98	21	119

Merged error: 6.9b

Counts

119 → 21

regimes684.0ms

Accuracy

57.5% (10.6b remaining)

Error of 17.8b against oracle of 7.2b and baseline of 32.2b

bsearch163.0ms

Steps

Iters	Range		Point
5	1.8171784245322648e+37	6.43616546702885e+37	3.3662626745557016e+37
9	2.361294668607769e-213	1.9980346609717805e-204	1.0126300995154855e-212
7	-2.410271475432134e-307	2.8466800401792686e-308	-2.8820882891916374e-308
6	-1.1149114536052807e+61	-7.527714714268046e+59	-2.0752208244632336e+60

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	114
1	64	114

end0.0ms

sample2.2s

Algorithm

intervals

Results

791.0ms	8000×	body	80	valid
743.0ms	7896×	body	80	nan

Details

sample80.0ms

simplify2.0ms

prune5.0ms

localize20.0ms

rewrite34.0ms

series74.0ms

simplify66.0ms

prune263.0ms

localize24.0ms

rewrite49.0ms

series76.0ms

simplify83.0ms

prune396.0ms

localize24.0ms

rewrite24.0ms

series77.0ms

simplify51.0ms

prune225.0ms

localize23.0ms

rewrite22.0ms

series106.0ms

simplify39.0ms

prune142.0ms

regimes684.0ms

bsearch163.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling