Details

Time bar (total: 6.8m)

sample656.0ms

Algorithm
intervals
Results
142.0ms164×body80valid
117.0ms53×body1280valid
68.0ms46×body640valid
32.0ms24×body320valid
9.0ms12×body160valid

simplify160.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
159.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (sin B))
0.1b
(/ x (tan B))
0.0b
(- (/ 1 (sin B)) (/ x (tan B)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
215×add-cube-cbrt
182×prod-diff
31×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
3 → 285
Calls
3 calls:
Slowest
38.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series366.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
184.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
154.0ms
(/ x (tan B))
27.0ms
(/ 1 (sin B))

simplify1.1m

Counts
456 → 294
Calls
456 calls:
Slowest
857.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
641.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
624.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
580.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
547.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (tan B) x))
0.2b
(/ (tan B) x)
0.2b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
1390×times-frac
881×add-sqr-sqrt
855×*-un-lft-identity
834×add-cube-cbrt
572×prod-diff
108×div-inv
21×add-exp-log
19×associate-/r*
15×difference-of-squares
14×associate-/r/
13×add-cbrt-cube fma-neg
10×div-exp
9×associate-/l*
7×distribute-lft-out--
6×pow1 add-log-exp
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp clear-num frac-2neg 1-exp
2×pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot frac-sub flip-- associate-/l/
Counts
4 → 767
Calls
4 calls:
Slowest
41.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ (tan B) x)
5.0ms
(/ 1 (sin B))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
122.0ms
(/ 1 (/ (tan B) x))
75.0ms
(/ (tan B) x)
22.0ms
(/ 1 (sin B))

simplify5.2m

Counts
1362 → 779
Calls
1362 calls:
Slowest
933.0ms
(fma (- (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))) (* (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x)))))
835.0ms
(fma (- (/ 1 (/ (cbrt (tan B)) (cbrt x)))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x)))) (* (/ 1 (/ (cbrt (tan B)) (cbrt x))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x))))))
809.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ (sqrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (sqrt 1) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))))))
754.0ms
(fma (- (/ (cbrt 1) (/ (sqrt (tan B)) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (sqrt x))) (* (/ (cbrt 1) (/ (sqrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (sqrt x)))))
734.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))

prune8.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ -1 (tan B))
0.2b
(/ 1 (sin B))
0.1b
(fma (/ -1 (tan B)) x (/ 1 (sin B)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg div-inv
1×rec-exp 1-exp tan-quot associate-/r/ fma-udef pow-flip inv-pow
Counts
3 → 76
Calls
3 calls:
Slowest
10.0ms
(/ 1 (sin B))
9.0ms
(/ -1 (tan B))
0.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))

series208.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
136.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))
57.0ms
(/ -1 (tan B))
14.0ms
(/ 1 (sin B))

simplify2.1s

Counts
62 → 85
Calls
62 calls:
Slowest
725.0ms
(/ (* (* -1 -1) -1) (* (* (tan B) (tan B)) (tan B)))
216.0ms
(- (+ (* 1/3 B) (* 1/45 (pow B 3))) (/ 1 B))
202.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
98.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
73.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (cos B) (sin B))
0.2b
(/ 1 (sin B))
0.1b
(fma (- (/ (cos B) (sin B))) x (/ 1 (sin B)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg div-inv
1×rec-exp 1-exp fma-udef pow-flip inv-pow
Counts
3 → 75
Calls
3 calls:
Slowest
17.0ms
(/ (cos B) (sin B))
10.0ms
(/ 1 (sin B))
0.0ms
(fma (- (/ (cos B) (sin B))) x (/ 1 (sin B)))

series203.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(fma (- (/ (cos B) (sin B))) x (/ 1 (sin B)))
36.0ms
(/ (cos B) (sin B))
25.0ms
(/ 1 (sin B))

simplify1.9s

Counts
61 → 84
Calls
61 calls:
Slowest
479.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
375.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
184.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
115.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
89.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune911.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.6s1786×body1280valid
2.4s1423×body640valid
1.4s4895×body80valid
575.0ms686×body320valid
218.0ms360×body160valid