Details

analyze453.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample43.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
3.0ms	31×	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

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: 32.2b

Counts

2 → 1

localize20.0ms

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))
29.9b	(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)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5011	2020

prune268.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 8.1b

Counts

123 → 14

localize25.0ms

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)
29.9b	(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:

5.0ms	(* (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)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
20.0ms	(pow (log base) 4)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5046	938

prune239.0ms

Filtered

65 candidates to 109 candidates (-67.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 8.1b

Counts

123 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
21.0ms	(cbrt base)
24.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4877	726
1	4877	726

prune188.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	74	19	93

Merged error: 8.1b

Counts

93 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

14.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4960	2097
1	4960	2097

prune172.0ms

Filtered

77 candidates to 116 candidates (-50.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	4	13	17
Picked	0	1	1
Done	0	1	1
Total	117	18	135

Merged error: 8.0b

Counts

135 → 18

regimes792.0ms

Accuracy

58.6% (10.3b remaining)

Error of 17.2b against oracle of 6.9b and baseline of 31.8b

bsearch150.0ms

Steps

Iters	Range		Point
7	2.0356440119917021e+130	3.2705810515858865e+131	5.451000501311567e+130
8	5.2335197312692986e-167	1.596171609383423e-164	3.212414840868755e-166
8	6.193178991784203e-254	1.6603718674917305e-249	1.7435253549818522e-250
4	-2.0907852145710102e+105	-1.4380819731206556e+105	-1.4992729020066265e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	122
1	78	122

end0.0ms

sample1.1s

Algorithm

intervals

Results

795.0ms	8000×	body	80	valid
94.0ms	1006×	body	80	nan

Details

analyze453.0ms

sample43.0ms

simplify3.0ms

prune5.0ms

localize20.0ms

rewrite27.0ms

series69.0ms

simplify73.0ms

prune268.0ms

localize25.0ms

rewrite19.0ms

series62.0ms

simplify45.0ms

prune239.0ms

localize25.0ms

rewrite13.0ms

series73.0ms

simplify50.0ms

prune188.0ms

localize22.0ms

rewrite30.0ms

series66.0ms

simplify45.0ms

prune172.0ms

regimes792.0ms

bsearch150.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling