Details

sample65.0ms

Algorithm

intervals

Results

24.0ms	282×	body	80	nan
22.0ms	256×	body	80	valid

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 34.9b

Counts

2 → 1

localize25.0ms

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))
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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:

10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
89.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	445	1362
1	1751	1236
2	5001	1205

prune441.0ms

Filtered

122 candidates to 84 candidates (68.9%)

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: 6.0b

Counts

123 → 17

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)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
163×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
141×	`sqrt-prod`
31×	`pow1`
24×	`associate-/l*`
18×	`sqrt-div`
16×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`flip3-+` `flip-+`
8×	`associate-r` `associate-l` `div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

18.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 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)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
150.0ms	(* (log base) (log base))
149.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify123.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	839	8779
1	3156	8145
2	5001	8032

prune739.0ms

Filtered

290 candidates to 136 candidates (46.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	288	2	290
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	291	16	307

Merged error: 6.0b

Counts

307 → 16

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)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
32.4b	(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:

14.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
88.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	569	1512
1	2601	1356
2	5002	1312

prune562.0ms

Filtered

133 candidates to 86 candidates (64.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	14	14
Picked	1	0	1
Done	0	1	1
Total	132	17	149

Merged error: 6.0b

Counts

149 → 17

localize26.0ms

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)
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

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:

8.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
165.0ms	(cbrt base)
168.0ms	(cbrt base)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	225	495
1	626	452
2	1627	429
3	5001	422

prune290.0ms

Filtered

77 candidates to 58 candidates (75.3%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	75	19	94

Merged error: 5.9b

Counts

94 → 19

regimes735.0ms

Accuracy

55.6% (10.9b remaining)

Error of 18.4b against oracle of 7.5b and baseline of 32.1b

bsearch298.0ms

Steps

Iters	Range		Point
9	1.5751293102757547e+115	7.140180388487143e+122	2.1705154911404016e+122
8	2.384370588866208e-253	3.0904878946447764e-249	3.92741566763516e-251
6	-1.924081377858164e-177	-1.5337444828711919e-178	-3.1005872008885e-178
9	-5.090921102564311e+75	-1.218226967287788e+68	-1.8575861199407474e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	93
1	75	93

end0.0ms

sample1.8s

Algorithm

intervals

Results

719.0ms	8000×	body	80	valid
686.0ms	8049×	body	80	nan