Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
16.0ms	256×	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: 35.0b

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))
0.6b	(* (log base) (log base))
32.4b	(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:

9.0ms	(/ (+ (* (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)))

series380.0ms

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)))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

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

prune468.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

10.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
89.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
293.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	443	1231
1	1594	1134
2	5001	1115

prune427.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `log-prod` `associate-l` `log-pow` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
150.0ms	(pow (log base) 2)
144.0ms	(pow (log base) 2)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify136.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	258	559
1	852	497
2	3702	477
3	5001	470

prune387.0ms

Filtered

93 candidates to 57 candidates (61.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
0.7b	(pow (* (log base) (log base)) 3)
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow1`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `pow-pow` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow2` `pow-unpow` `pow-plus` `pow-prod-down` `prod-exp` `sqrt-prod` `pow-sqr` `pow-prod-up` `cbrt-unprod`
2×	`sqrt-div` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `cube-prod` `flip-+` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

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

series520.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
189.0ms	(pow (* (log base) (log base)) 3)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	244	471
1	941	424
2	5001	405

prune419.0ms

Filtered

125 candidates to 71 candidates (56.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.9b

regimes641.0ms

Accuracy

56.9% (10.7b remaining)

Error of 18.3b against oracle of 7.6b and baseline of 32.4b

bsearch267.0ms

Steps

Iters	Range		Point
6	8.038692978176935e+71	4.059966308836584e+72	3.250300518593509e+72
10	3.1166165557256147e-245	2.1203349454453513e-228	4.7123917155526997e-237
5	-3.6529095553677684e-184	-9.145947984649642e-185	-1.2768762773806977e-184
8	-2.262192332260186e+49	-6.874003963443684e+46	-7.820663461952384e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	75
1	62	75

end0.0ms

sample1.4s

Algorithm

intervals

Results

538.0ms	8000×	body	80	valid
515.0ms	7947×	body	80	nan