Details

sample71.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
21.0ms	236×	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

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: 33.3b

Counts

2 → 1

localize19.0ms

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))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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))
10.0ms	(/ (+ (* (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))
7.0ms	(sqrt (+ (* re re) (* im im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
24.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	457	1397
1	1716	1276
2	5001	1225

prune251.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

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: 7.9b

Counts

123 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 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))
30.9b	(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)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ 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)))))
18.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	687	3341
1	3728	2983
2	5001	2817

prune336.0ms

Filtered

102 candidates to 186 candidates (-82.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	180	6	186
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	184	19	203

Merged error: 7.8b

Counts

203 → 19

localize21.0ms

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))
1.3b	(pow (log base) 6)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

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:

10.0ms	(/ (+ (* (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))
2.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
14.0ms	(cbrt (pow (log base) 6))
22.0ms	(pow (log base) 6)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	408	1091
1	1442	1003
2	5001	979

prune241.0ms

Filtered

65 candidates to 92 candidates (-41.5%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	90	21	111

Merged error: 7.8b

Counts

111 → 21

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
30.9b	(sqrt (+ (* re re) (* im im)))
32.0b	(log (+ (* re re) (* im im)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(log (+ (* re re) (* im im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt base)
22.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(log (+ (* re re) (* im im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	184	328
1	378	301
2	840	276
3	2309	273
4	5001	273

prune82.0ms

Filtered

51 candidates to 63 candidates (-23.5%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	19	19
Picked	0	1	1
Done	0	1	1
Total	63	21	84

Merged error: 7.8b

Counts

84 → 21

regimes810.0ms

Accuracy

55.6% (11.1b remaining)

Error of 18.5b against oracle of 7.4b and baseline of 32.4b

bsearch147.0ms

Steps

Iters	Range		Point
6	745734302528.237	4360532195325.5825	3954432402615.8184
7	2.498572685790142e-207	4.3079410964264224e-206	3.6254561911357347e-206
8	3.8664896185117035e-261	7.747425441946343e-257	2.7161845734571728e-257
4	-4.195944497724489e+76	-2.4357687759714265e+76	-4.1265942109521596e+76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	96
1	73	96

end0.0ms

sample1.8s

Algorithm

intervals

Results

752.0ms	8000×	body	80	valid
591.0ms	6656×	body	80	nan

Details

sample71.0ms

simplify4.0ms

prune4.0ms

localize19.0ms

rewrite31.0ms

series66.0ms

simplify59.0ms

prune251.0ms

localize25.0ms

rewrite47.0ms

series70.0ms

simplify95.0ms

prune336.0ms

localize21.0ms

rewrite20.0ms

series67.0ms

simplify47.0ms

prune241.0ms

localize29.0ms

rewrite10.0ms

series58.0ms

simplify81.0ms

prune82.0ms

regimes810.0ms

bsearch147.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling