Details

sample61.0ms

Algorithm

intervals

Results

22.0ms	268×	body	80	nan
17.0ms	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: 33.3b

localize19.0ms

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) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

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:

37.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
87.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
150.0ms	(* (log base) (log base))
37.0ms	(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

prune449.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.6b

localize25.0ms

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))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
139.0ms	(* (log base) (log base))
145.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify152.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (143.0ms)

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

prune428.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

10.0ms	(* (log base) (log base))
1.0ms	(cbrt base)
4.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (log base) (log base))
330.0ms	(cbrt base)
176.0ms	(cbrt base)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	212	331
1	679	298
2	2893	277
3	5002	269

prune436.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(cbrt (pow (log base) 6))
3.0ms	(pow (log base) 6)
8.0ms	(sqrt (+ (* re re) (* im im)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
148.0ms	(cbrt (pow (log base) 6))
178.0ms	(pow (log base) 6)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	278	602
1	880	553
2	3605	514
3	5002	512

prune295.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 10.5b

regimes532.0ms

Accuracy

58.1% (10.2b remaining)

Error of 17.6b against oracle of 7.5b and baseline of 31.7b

bsearch354.0ms

Steps

Iters	Range		Point
10	2.8357154741625015e+84	5.970052819679034e+96	3.028881099794191e+96
8	1.3109469629400665e-202	1.7298187667743967e-198	5.301603919361751e-202
8	-2.127201098816139e-283	-3.724416781071774e-287	-1.097857316006781e-283
8	-2.4246649145524328e+112	-6.571063900108181e+109	-1.5825984745485794e+112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	107
1	76	107

end0.0ms

sample1.6s

Algorithm

intervals

Results

557.0ms	7964×	body	80	nan
552.0ms	8000×	body	80	valid