Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
18.0ms	253×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

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)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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:

13.0ms	(/ (+ (* (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))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
156.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

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

prune483.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.8b

localize22.0ms

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))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

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))
4.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
153.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify150.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (142.0ms)

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

prune448.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
33.0b	(cbrt (+ (* re re) (* im im)))
33.0b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
8×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
6×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in`
4×	`cbrt-div` `add-log-exp`
2×	`pow2` `flip3-+` `pow-plus` `pow1/3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

4.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
92.0ms	(cbrt (+ (* re re) (* im im)))
236.0ms	(cbrt (+ (* re re) (* im im)))

simplify120.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	216	548
1	792	486
2	3678	458
3	5001	442

prune487.0ms

Filtered

110 candidates to 64 candidates (58.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
32.0b	(sqrt (+ (* re re) (* im im)))
33.2b	(log (+ (* re re) (* im im)))

rewrite8.0ms

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:

0.0ms	(cbrt base)
0.0ms	(cbrt base)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(log (+ (* re re) (* im im)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt base)
176.0ms	(cbrt base)
41.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(log (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 4 (66.0ms)

Iter	Nodes	Cost
0	167	300
1	354	275
2	818	271
3	2399	271
4	5001	270

prune366.0ms

Filtered

63 candidates to 53 candidates (84.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 9.8b

regimes657.0ms

Accuracy

56.6% (10.7b remaining)

Error of 18.3b against oracle of 7.6b and baseline of 32.3b

bsearch278.0ms

Steps

Iters	Range		Point
8	8.503002622430935e+53	4.277142149416969e+57	5.945116929153346e+55
6	3.428006992635784e-285	4.5097690370146326e-284	3.510677278861231e-284
9	-1.438807227410586e-183	-3.1793237657503557e-190	-4.2771113256202204e-185
8	-6.345330674033112e+21	-7.616424799926762e+18	-1.1225739876249368e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	98
1	60	98

end0.0ms

sample1.5s

Algorithm

intervals

Results

568.0ms	8212×	body	80	nan
537.0ms	8000×	body	80	valid