Details

sample1.2s

Algorithm

intervals

Results

915.0ms	105×	body	1280	valid
119.0ms	48×	body	640	valid
73.0ms	24×	body	320	valid
34.0ms	70×	body	80	valid
10.0ms	9×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	64
3	64
2	59
1	36
0	22

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (sin delta)) (cos theta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

45.0ms	(* (* (cos phi1) (sin delta)) (cos theta))
30.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (* (cos phi1) (sin delta)) (cos theta))
228.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
257.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.1s

Counts

83 → 83

Iterations

Iter	Nodes
3	3370
2	1001
1	365
0	159

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize143.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(fma 1 (cos delta) (- (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
55.3b	(fma (- (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`asin-acos` `fma-udef`

Counts

4 → 40

Calls

4 calls:

4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms	(fma 1 (cos delta) (- (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
0.0ms	(fma (- (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
259.0ms	(fma 1 (cos delta) (- (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
308.0ms	(fma (- (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify1.7s

Counts

52 → 52

Iterations

Iter	Nodes
4	3464
3	1208
2	356
1	158
0	87

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize127.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (* (* (cos phi1) (sin delta)) (cos theta)))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`asin-acos` `log1p-udef` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

0.0ms	(log1p (* (* (cos phi1) (sin delta)) (cos theta)))
18.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta))))))))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(log1p (* (* (cos phi1) (sin delta)) (cos theta)))
263.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta))))))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta))))))
280.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (expm1 (log1p (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
3	2141
2	794
1	327
0	151

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))))))
0.3b	(asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))
0.5b	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1)))))))))
3.3b	(log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`sin-sum`
7×	`pow1`
6×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `add-exp-log` `associate--r+` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l` `prod-diff`
2×	`asin-acos`
1×	`log-div` `sub-neg` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

20.0ms	(* (sin phi1) (sin (log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))))))
1.0ms	(asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))
13.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1)))))))))
3.0ms	(log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(* (sin phi1) (sin (log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))))))
6.0ms	(asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))
241.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1)))))))))
10.0ms	(log (exp (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (cos delta) (sin phi1))))))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
3	2570
2	974
1	403
0	187

prune2.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes790.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify22.0ms

Iterations

Iter	Nodes
3	40
2	40
1	38
0	28

end0.0ms

sample26.9s

Algorithm

intervals

Results

15.2s	3125×	body	1280	valid
7.3s	1851×	body	640	valid
2.0s	714×	body	320	valid
1.6s	1996×	body	80	valid
348.0ms	314×	body	160	valid