Details

Time bar (total: 51.9s)

sample432.0ms

Algorithm
intervals
Results
274.0ms96×body1280valid
96.0ms67×body640valid
18.0ms74×body80valid
13.0ms15×body320valid
3.0ms4×body160valid

simplify66.0ms

Counts
1 → 1
Iterations
IterNodes
done64
364
259
136
022

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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 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:
30.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
14.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
204.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
233.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.1s

Counts
87 → 87
Iterations
IterNodes
done5000
34278
21107
1372
0163

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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:
27.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
7.0ms
(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))))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
6.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
224.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
283.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify3.5s

Counts
87 → 87
Iterations
IterNodes
done5004
33385
21011
1377
0170

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize173.0ms

Local error

Found 4 expressions with local error:

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

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
21×sin-mult
20×add-cbrt-cube add-exp-log
19×pow-prod-down associate-*l/
12×add-sqr-sqrt
10×prod-exp cos-mult cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l* frac-sub
6×frac-times associate-*r/ add-log-exp
4×expm1-log1p-u pow-sqr pow-prod-up insert-posit16 log1p-expm1-u
3×*-commutative sub-div
2×pow-plus pow3 unswap-sqr
1×pow2 difference-cubes sub-neg flip3-- fma-neg diff-log swap-sqr prod-diff flip--
Counts
4 → 112
Calls
4 calls:
13.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
17.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
302.0ms
(- (* (* (cos delta) (cos delta)) (cos delta)) (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))
72.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
239.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
235.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
980.0ms
(- (* (* (cos delta) (cos delta)) (cos delta)) (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))
297.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))

simplify3.0s

Counts
124 → 124
Iterations
IterNodes
done5003
22817
1725
0231

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize254.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* (* (cos delta) (cos delta)) (cos delta)) (* (cbrt (* (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))
0.3b
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))
0.3b
(* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
10.6b
(cbrt (* (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
297×associate-*l/
278×sin-mult
179×frac-times
93×cbrt-div
72×associate-*r/
64×cos-mult
63×frac-sub
50×pow1
20×pow-prod-down
18×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
6×add-log-exp
5×pow-sqr pow-prod-up
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u
3×pow-plus pow3
2×pow2 *-commutative
1×cbrt-prod sub-neg flip3-- fma-neg pow1/3 diff-log prod-diff rem-cbrt-cube sqr-sin flip-- sub-div unswap-sqr
Counts
4 → 195
Calls
4 calls:
1.4s
(- (* (* (cos delta) (cos delta)) (cos delta)) (* (cbrt (* (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))
60.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))
27.0ms
(* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
1.3s
(cbrt (* (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
970.0ms
(- (* (* (cos delta) (cos delta)) (cos delta)) (* (cbrt (* (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))))
280.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))
209.0ms
(* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))
262.0ms
(cbrt (* (* (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (cos delta) (sin phi1)))))))))

simplify5.0s

Counts
207 → 207
Iterations
IterNodes
done5003
11674
0544

prune4.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes886.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done27
127
021

end0.0ms

sample19.2s

Algorithm
intervals
Results
12.6s3144×body1280valid
4.0s1900×body640valid
1.3s690×body320valid
730.0ms1967×body80valid
268.0ms299×body160valid