Details

sample74.0ms

Algorithm

intervals

Results

28.0ms	265×	body	80	nan
28.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (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))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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))
13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune469.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

localize22.0ms

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))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

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:

28.0ms	(/ (/ (+ (* (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))))
4.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (+ (* (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))))
149.0ms	(* (log base) (log base))
150.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify122.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (56.0ms)

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

prune844.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.0b	(cbrt (+ (* re re) (* im im)))
29.0b	(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

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)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (log base) (log base))
149.0ms	(* (log base) (log base))
93.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify119.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (112.0ms)

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

prune464.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.0b	(cbrt (+ (* re re) (* im im)))
31.4b	(pow (+ (* re re) (* im im)) 1/3)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
23×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`add-exp-log`
8×	`associate-r` `associate-l` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow`
2×	`pow2` `cbrt-div` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 103

Calls

4 calls:

4.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
2.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(pow (+ (* re re) (* im im)) 1/3)

series492.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (log base) (log base))
151.0ms	(* (log base) (log base))
94.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(pow (+ (* re re) (* im im)) 1/3)

simplify40.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	266	539
1	1053	465
2	5002	439

prune461.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 6.6b

regimes467.0ms

Accuracy

58.7% (10.3b remaining)

Error of 17.9b against oracle of 7.6b and baseline of 32.5b

bsearch100.0ms

Steps

Iters	Range		Point
6	2.1975248708397488e+49	2.8538281382745483e+50	2.6939685274605205e+50
3	-4.016526982298196e+69	-2.8842780556144676e+69	-3.910349229519163e+69

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	49
1	55	49

end0.0ms

sample2.0s

Algorithm

intervals

Results

901.0ms	8000×	body	80	valid
750.0ms	7750×	body	80	nan