Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
5.0ms	28×	body	2560	valid
3.0ms	12×	body	5120	valid
2.0ms	15×	body	1280	valid
1.0ms	10×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 40

Calls

3 calls:

14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune150.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
16.5b	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
7×	`sqrt-prod`
6×	`sqrt-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `flip3-+` `associate-*r/` `flip-+`
3×	`pow-unpow` `sqrt-pow1`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 83

Calls

4 calls:

12.0ms	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
3.0ms	(sqrt (+ (* re re) (* im im)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

448.0ms	(pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3)
45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
182.0ms	(cbrt (pow (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))) 3))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	433	886
1	1632	846
2	5001	828

prune240.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.2b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
33.7b	(cbrt (+ (* re re) (* im im)))
33.7b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

12.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
81.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
93.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	323	928
1	1214	868
2	5002	841

prune284.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.1b

localize17.0ms

Local error

Found 4 expressions with local error:

6.2b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
32.6b	(sqrt (+ (* re re) (* im im)))
32.6b	(sqrt (+ (* re re) (* im im)))
33.7b	(cbrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

28.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	274	690
1	967	619
2	3189	582
3	5002	580

prune272.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.1b

regimes526.0ms

Accuracy

59.3% (8.3b remaining)

Error of 26.3b against oracle of 18.1b and baseline of 38.4b

bsearch83.0ms

Steps

Iters	Range		Point
8	1.704068108985656e+134	2.397866045703051e+137	1.164285257168749e+137
9	-4.2891484322939016e-225	-5.158097903870568e-234	-5.303374603508321e-234

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	22
1	37	22

end0.0ms

sample666.0ms

Algorithm

intervals

Results

196.0ms	6012×	body	80	valid
125.0ms	635×	body	2560	valid
79.0ms	337×	body	5120	valid
72.0ms	466×	body	1280	valid
42.0ms	299×	body	640	valid
17.0ms	147×	body	320	valid
6.0ms	104×	body	160	valid