Details

sample671.0ms

Algorithm

intervals

Results

240.0ms	62×	body	640	valid
231.0ms	83×	body	1280	valid
27.0ms	25×	body	320	valid
21.0ms	70×	body	80	valid
11.0ms	16×	body	160	valid

simplify424.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

423.0ms

(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize56.0ms

Local error

Found 3 expressions with local error:

1.7b	(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
0.2b	(* (sin th) (sin ky))
0.1b	(hypot (sin kx) (sin ky))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `sin-mult`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

3 → 58

Calls

3 calls:

Slowest

19.0ms	(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
11.0ms	(* (sin th) (sin ky))
0.0ms	(hypot (sin kx) (sin ky))

series1.1s

Counts

3 → 9

Calls

3 calls:

Slowest

871.0ms	(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
144.0ms	(hypot (sin kx) (sin ky))
83.0ms	(* (sin th) (sin ky))

simplify3.9s

Counts

71 → 67

Calls

71 calls:

Slowest

382.0ms	(* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky)))
380.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
378.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
361.0ms	(* (* (/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky))) (/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))) (/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky))))
270.0ms	(* (* (* (sin th) (sin ky)) (* (sin th) (sin ky))) (* (sin th) (sin ky)))

prune898.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b	(hypot (sin kx) (sin ky))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

Slowest

32.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
16.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series782.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

369.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
244.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
168.0ms	(hypot (sin kx) (sin ky))

simplify6.3s

Counts

96 → 85

Calls

96 calls:

Slowest

525.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
473.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
459.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
358.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
333.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (hypot (sin kx) (sin ky))))
0.2b	(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky))))))
0.2b	(/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky)))))
0.2b	(log1p (hypot (sin kx) (sin ky)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `log1p-expm1` `associate-r/` `-commutative` `expm1-udef`

Counts

4 → 89

Calls

4 calls:

Slowest

34.0ms	(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky))))))
16.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky)))))
1.0ms	(log1p (hypot (sin kx) (sin ky)))
1.0ms	(expm1 (log1p (hypot (sin kx) (sin ky))))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

390.0ms	(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky))))))
279.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky)))))
202.0ms	(expm1 (log1p (hypot (sin kx) (sin ky))))
177.0ms	(log1p (hypot (sin kx) (sin ky)))

simplify7.4s

Counts

110 → 101

Calls

110 calls:

Slowest

526.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
495.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
432.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (expm1 (log1p (hypot (sin kx) (sin ky)))) (expm1 (log1p (hypot (sin kx) (sin ky))))) (expm1 (log1p (hypot (sin kx) (sin ky))))))
369.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
347.0ms	(log (+ (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) 1))

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
0.2b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

17.0ms	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
16.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
1.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

331.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
298.0ms	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
286.0ms	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))
246.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify6.6s

Counts

95 → 87

Calls

95 calls:

Slowest

471.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
462.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
420.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
406.0ms	(log (+ (* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky)) 1))
371.0ms	(- (+ (* 7/60 (pow ky 4)) (* 1/6 (* kx ky))) (* 1/6 (pow ky 2)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.9b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 8.6b against oracle of 8.4b and baseline of 8.6b

bsearch2.0ms

end0.0ms

sample12.0s

Algorithm

intervals

Results

6.8s	2706×	body	1280	valid
3.1s	1800×	body	640	valid
880.0ms	765×	body	320	valid
728.0ms	2397×	body	80	valid
263.0ms	332×	body	160	valid