Details

Time bar (total: 41.6s)

sample517.0ms

Algorithm
intervals
Results
279.0ms96×body1280valid
92.0ms59×body640valid
82.0ms22×body320valid
20.0ms68×body80valid
7.0ms11×body160valid

simplify92.0ms

Counts
1 → 1
Iterations
IterNodes
done75
475
373
261
136
022

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (* (cos phi1) (sin delta)))
0.2b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite80.0ms

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-*l* add-log-exp
4×expm1-log1p-u associate-*r* 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:
46.0ms
(* (sin theta) (* (cos phi1) (sin delta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
19.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
11.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series652.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* (sin theta) (* (cos phi1) (sin delta)))
7.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
217.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
316.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.6s

Counts
83 → 83
Iterations
IterNodes
done5000
21475
1370
0164

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize140.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (* (cos phi1) (sin delta)))
0.2b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
9×prod-diff
7×add-log-exp
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-neg
2×diff-log *-commutative
1×asin-acos log1p-udef sub-neg flip3-- flip-- sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 80
Calls
4 calls:
21.0ms
(* (sin theta) (* (cos phi1) (sin delta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
27.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
12.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (sin theta) (* (cos phi1) (sin delta)))
10.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
242.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
346.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

simplify2.1s

Counts
92 → 92
Iterations
IterNodes
done5000
21655
1409
0187

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (* (cos phi1) (sin delta)))
0.2b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
9×prod-diff
7×add-log-exp
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-neg
2×diff-log *-commutative
1×asin-acos log1p-udef sub-neg flip3-- flip-- sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 80
Calls
4 calls:
20.0ms
(* (sin theta) (* (cos phi1) (sin delta)))
0.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
13.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
6.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (sin theta) (* (cos phi1) (sin delta)))
7.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
238.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
353.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

simplify2.0s

Counts
92 → 92
Iterations
IterNodes
done5000
21655
1409
0187

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize230.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.3b
(/ (- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))) (+ (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))
0.3b
(* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
0.4b
(- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
24×add-sqr-sqrt
20×add-cube-cbrt
16×times-frac
13×pow1
10×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp difference-of-squares
5×distribute-lft-out
4×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
3×swap-sqr
2×flip3-- pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod flip-- unswap-sqr associate-/l/
1×pow2 cbrt-undiv sqr-cos clear-num sub-neg frac-2neg flip3-+ pow-plus fma-neg diff-log div-sub div-exp prod-diff associate--l+ pow-sqr pow-prod-up flip-+ div-inv sin-mult
Counts
4 → 109
Calls
4 calls:
10.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
33.0ms
(/ (- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))) (+ (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))
5.0ms
(* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
11.0ms
(- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))

series2.6s

Counts
4 → 12
Calls
4 calls:
283.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.2s
(/ (- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))) (+ (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))
432.0ms
(* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
725.0ms
(- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))

simplify3.2s

Counts
121 → 121
Iterations
IterNodes
done5000
24622
1737
0259

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify19.0ms

Iterations
IterNodes
done38
138
031

end0.0ms

sample19.6s

Algorithm
intervals
Results
11.7s3083×body1280valid
4.9s1902×body640valid
957.0ms1984×body80valid
889.0ms720×body320valid
686.0ms311×body160valid