Details

analyze447.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
5.0ms	27×	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: 32.6b

Counts

2 → 1

localize19.0ms

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))
30.1b	(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:

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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
26.0ms	(/ (+ (* (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)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

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

prune219.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	12	123

Merged error: 7.0b

Counts

123 → 12

localize20.0ms

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)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`pow1`
23×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod`
11×	`times-frac`
10×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv`

Counts

4 → 121

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
7.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
24.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	581	1547
1	2548	1393
2	5001	1339

prune188.0ms

Filtered

82 candidates to 133 candidates (-62.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	131	14	145

Merged error: 7.0b

Counts

145 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.5b	(cbrt base)
0.5b	(cbrt base)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
21.0ms	(cbrt base)
25.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	384	1340
1	1264	1221
2	5001	1183

prune188.0ms

Filtered

66 candidates to 80 candidates (-21.2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	77	17	94

Merged error: 6.9b

Counts

94 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.8b	(pow (log base) 3)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `log-pow`
10×	`associate-l`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`unpow-prod-down` `cube-prod` `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` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `unpow3` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
20.0ms	(pow (log base) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	346	655
1	1782	586
2	5001	540

prune145.0ms

Filtered

65 candidates to 116 candidates (-78.5%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	1	13	14
Picked	0	1	1
Done	0	2	2
Total	115	18	133

Merged error: 6.9b

Counts

133 → 18

regimes753.0ms

Accuracy

57.1% (10.7b remaining)

Error of 17.9b against oracle of 7.1b and baseline of 32.1b

bsearch1.1s

Steps

Iters	Range		Point
9	1.8071784385087965e+88	1.956352872949379e+95	2.991115121984362e+92
10	2.03445239337126e-243	1.4119716713952674e-230	1.7914312298790939e-236
9	-4.986974733076275e-283	-6.128806631199907e-291	-1.8365258186749333e-284
9	-3.2622547551435643e+125	-8.144013196330302e+116	-1.8097299752127242e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	71
1	88	71
2	88	71

end0.0ms

analyze444.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

778.0ms	8000×	body	80	valid
98.0ms	1003×	body	80	nan

Details

analyze447.0ms

sample40.0ms

simplify4.0ms

prune4.0ms

localize19.0ms

rewrite26.0ms

series67.0ms

simplify57.0ms

prune219.0ms

localize20.0ms

rewrite32.0ms

series64.0ms

simplify78.0ms

prune188.0ms

localize26.0ms

rewrite20.0ms

series98.0ms

simplify47.0ms

prune188.0ms

localize28.0ms

rewrite19.0ms

series60.0ms

simplify61.0ms

prune145.0ms

regimes753.0ms

bsearch1.1s

simplify2.0ms

end0.0ms

analyze444.0ms

sample1.1s

Profiling