Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	301×	body	80	nan
18.0ms	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: 32.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))
29.7b	(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:

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))
4.0ms	(sqrt (+ (* re re) (* im im)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
150.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune603.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 7.0b

Counts

123 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

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

series422.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
148.0ms	(* (log base) (log base))
146.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify158.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592

prune390.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	127	15	142

Merged error: 7.0b

Counts

142 → 15

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

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

series429.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
154.0ms	(* (log base) (log base))
149.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify158.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	262	720
1	966	639
2	4681	599
3	5001	592

prune420.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	3	10	13
Picked	0	1	1
Done	1	0	1
Total	127	15	142

Merged error: 7.0b

Counts

142 → 15

localize27.0ms

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)))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.7b	(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)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (+ (* (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)))
175.0ms	(cbrt base)
175.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	366	1306
1	1283	1187
2	5001	1169

prune380.0ms

Filtered

80 candidates to 67 candidates (83.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	78	17	95

Merged error: 7.0b

Counts

95 → 17

regimes614.0ms

Accuracy

56.8% (10.7b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 32.0b

bsearch334.0ms

Steps

Iters	Range		Point
8	8.889439910526904e+123	3.5273752339794244e+127	6.6271176197446635e+125
10	3.550777697600512e-293	8.557386595852449e-281	2.6641461174894536e-290
9	-2.5166973787667145e-191	-3.3540194544048986e-196	-3.387938572634905e-196
9	-2.0479593073330602e+104	-1.6090322379726622e+98	-9.61097156681763e+103

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	90
1	92	90
2	93	90
3	93	90

end0.0ms

sample1.5s

Algorithm

intervals

Results

579.0ms	8000×	body	80	valid
567.0ms	8117×	body	80	nan

Details

sample58.0ms

simplify4.0ms

prune4.0ms

localize24.0ms

rewrite27.0ms

series377.0ms

simplify66.0ms

prune603.0ms

localize23.0ms

rewrite23.0ms

series422.0ms

simplify158.0ms

prune390.0ms

localize28.0ms

rewrite23.0ms

series429.0ms

simplify158.0ms

prune420.0ms

localize27.0ms

rewrite20.0ms

series570.0ms

simplify47.0ms

prune380.0ms

regimes614.0ms

bsearch334.0ms

simplify3.0ms

end0.0ms

sample1.5s

Profiling