Details

Time bar (total: 49.9s)

sample758.0ms

Algorithm
intervals
Results
451.0ms94×body1280valid
192.0ms59×body640valid
52.0ms29×body320valid
25.0ms64×body80valid
10.0ms10×body160valid

simplify39.0ms

Counts
1 → 1
Iterations
IterNodes
464
364
259
136
022

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize454.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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 insert-posit16 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 → 75
Calls
4 calls:
14.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
31.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
95.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
12.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
246.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.1s

Counts
87 → 87
Iterations
IterNodes
33137
2998
1373
0170

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize142.0ms

Local error

Found 4 expressions with local error:

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

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
50×pow1
20×add-cbrt-cube add-exp-log
19×add-sqr-sqrt
18×pow-prod-down
17×*-un-lft-identity add-cube-cbrt
16×sin-mult
12×times-frac
11×cos-mult
9×prod-exp cbrt-unprod
7×associate-/l/
6×frac-sub add-log-exp
5×associate-*l/ associate-*r/ pow-sqr pow-prod-up difference-of-squares
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* sub-div
3×frac-times associate-/r* pow-plus
2×pow2 sqr-cos flip3-- associate-/r/ *-commutative flip--
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff associate--l+ flip-+ div-inv unswap-sqr
Counts
4 → 138
Calls
4 calls:
20.0ms
(* (cos delta) (cos delta))
57.0ms
(* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
82.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
78.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (cos delta) (cos delta))
307.0ms
(* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
949.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
582.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

simplify2.1s

Counts
150 → 150
Iterations
IterNodes
23088
1807
0286

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize148.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
154×pow1
40×pow-prod-down pow-prod-up
30×add-cbrt-cube add-exp-log
26×pow-sqr
20×pow-plus
19×add-sqr-sqrt
16×prod-exp cbrt-unprod
14×pow2 *-un-lft-identity add-cube-cbrt
12×times-frac
6×add-log-exp
5×difference-of-squares
4×expm1-log1p-u cos-mult insert-posit16 log1p-expm1-u sin-mult associate-/l*
3×associate-/r* prod-diff
2×frac-times flip3-- swap-sqr associate-*r* associate-*l* associate-*l/ associate-*r/ *-commutative flip-- associate-/l/
1×cbrt-undiv sqr-cos clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp associate--l+ fma-udef div-inv associate--r+ unswap-sqr
Counts
4 → 168
Calls
4 calls:
57.0ms
(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
21.0ms
(/ (- (* (cos delta) (cos delta)) (fma (* (* (* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1))) (sin delta)) (sin delta)) (* (sin phi1) (sin phi1)) (fma (* (cos delta) (cos delta)) (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (sin delta)) (+ (* (* (cos delta) (cos phi1)) (cos theta)) (* (* (cos delta) (cos phi1)) (cos theta))))))) (fma (* (sin phi1) (sin phi1)) (cos delta) (fma (* (sin delta) (* (cos phi1) (cos theta))) (sin phi1) (cos delta))))
73.0ms
(* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1)))
21.0ms
(- (* (cos delta) (cos delta)) (fma (* (* (* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1))) (sin delta)) (sin delta)) (* (sin phi1) (sin phi1)) (fma (* (cos delta) (cos delta)) (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (sin delta)) (+ (* (* (cos delta) (cos phi1)) (cos theta)) (* (* (cos delta) (cos phi1)) (cos theta)))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
1.2s
(/ (- (* (cos delta) (cos delta)) (fma (* (* (* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1))) (sin delta)) (sin delta)) (* (sin phi1) (sin phi1)) (fma (* (cos delta) (cos delta)) (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (sin delta)) (+ (* (* (cos delta) (cos phi1)) (cos theta)) (* (* (cos delta) (cos phi1)) (cos theta))))))) (fma (* (sin phi1) (sin phi1)) (cos delta) (fma (* (sin delta) (* (cos phi1) (cos theta))) (sin phi1) (cos delta))))
96.0ms
(* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1)))
672.0ms
(- (* (cos delta) (cos delta)) (fma (* (* (* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1))) (sin delta)) (sin delta)) (* (sin phi1) (sin phi1)) (fma (* (cos delta) (cos delta)) (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (sin delta)) (+ (* (* (cos delta) (cos phi1)) (cos theta)) (* (* (cos delta) (cos phi1)) (cos theta)))))))

simplify1.5s

Counts
180 → 180
Iterations
IterNodes
22812
1785
0291

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize136.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (cos delta) (* (* (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
5.2b
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
5.2b
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
5.2b
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-prod cbrt-div fma-neg pow1/3 prod-diff sin-mult
1×sub-neg flip3-- diff-log flip--
Counts
4 → 60
Calls
4 calls:
8.0ms
(- (cos delta) (* (* (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
10.0ms
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
10.0ms
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
11.0ms
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
245.0ms
(- (cos delta) (* (* (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
387.0ms
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
364.0ms
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
399.0ms
(cbrt (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify3.3s

Counts
72 → 72
Iterations
IterNodes
45597
31943
2666
1275
0117

prune961.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes638.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify29.0ms

Iterations
IterNodes
247
147
035

end0.0ms

sample27.4s

Algorithm
intervals
Results
15.8s3091×body1280valid
7.3s1920×body640valid
1.6s761×body320valid
1.5s1923×body80valid
823.0ms305×body160valid