Details

Time bar (total: 6.9m)

sample245.0ms

Algorithm
intervals
Results
111.0ms53×body1280valid
49.0ms46×body640valid
44.0ms164×body80valid
18.0ms24×body320valid
6.0ms12×body160valid

simplify136.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
136.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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)))

rewrite82.0ms

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
59.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series352.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
168.0ms
(/ x (tan B))
156.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
27.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
963.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
808.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
597.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
586.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
542.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)))

rewrite85.0ms

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
37.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms
(/ 1 (sin B))
6.0ms
(/ 1 (/ (tan B) x))
5.0ms
(/ (tan B) x)

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
109.0ms
(/ 1 (/ (tan B) x))
62.0ms
(/ (tan B) x)
18.0ms
(/ 1 (sin B))

simplify5.4m

Counts
1362 → 779
Calls
1362 calls:
Slowest
1.1s
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))
929.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ (cbrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))))))
788.0ms
(fma (- (/ 1 (/ (tan B) (sqrt x)))) (/ 1 (/ 1 (sqrt x))) (* (/ 1 (/ (tan B) (sqrt x))) (/ 1 (/ 1 (sqrt x)))))
758.0ms
(fma (- (/ (sqrt 1) (/ (tan B) (cbrt x)))) (/ (sqrt 1) (/ 1 (* (cbrt x) (cbrt x)))) (* (/ (sqrt 1) (/ (tan B) (cbrt x))) (/ (sqrt 1) (/ 1 (* (cbrt x) (cbrt x))))))
715.0ms
(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))))))

prune5.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite11.0ms

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
5.0ms
(/ 1 (sin B))
5.0ms
(/ -1 (tan B))
0.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))

series163.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
109.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))
39.0ms
(/ -1 (tan B))
16.0ms
(/ 1 (sin B))

simplify1.6s

Counts
62 → 85
Calls
62 calls:
Slowest
481.0ms
(/ (* (* -1 -1) -1) (* (* (tan B) (tan B)) (tan B)))
161.0ms
(- (+ (* 1/3 B) (* 1/45 (pow B 3))) (/ 1 B))
153.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
94.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
63.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune700.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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)))

rewrite15.0ms

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
9.0ms
(/ (cos B) (sin B))
5.0ms
(/ 1 (sin B))
0.0ms
(fma (- (/ (cos B) (sin B))) x (/ 1 (sin B)))

series151.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
112.0ms
(fma (- (/ (cos B) (sin B))) x (/ 1 (sin B)))
23.0ms
(/ (cos B) (sin B))
16.0ms
(/ 1 (sin B))

simplify1.5s

Counts
61 → 84
Calls
61 calls:
Slowest
311.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
295.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
153.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
92.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
63.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune699.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.4s1786×body1280valid
2.1s1423×body640valid
958.0ms4895×body80valid
883.0ms686×body320valid
134.0ms360×body160valid