Details

Time bar (total: 9.3m)

sample233.0ms

Algorithm
intervals
Results
75.0ms48×body1280valid
60.0ms51×body640valid
53.0ms155×body80valid
22.0ms28×body320valid
6.0ms12×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: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

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
42.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series300.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
157.0ms
(/ x (tan B))
125.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
18.0ms
(/ 1 (sin B))

simplify1.3m

Counts
504 → 294
Calls
504 calls:
Slowest
972.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
824.0ms
(- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B))))
732.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))))))
682.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
652.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
107×add-sqr-sqrt
105×*-un-lft-identity
98×add-cube-cbrt
91×prod-diff
28×div-inv
15×add-exp-log
13×add-cbrt-cube fma-neg
7×pow1
6×associate-/r* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u associate-/l*
3×cbrt-undiv distribute-rgt-out-- associate-*r* associate-*l* difference-of-squares
2×clear-num frac-2neg prod-exp cbrt-unprod distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div unswap-sqr
Counts
4 → 208
Calls
4 calls:
Slowest
35.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
15.0ms
(/ (* x (cos B)) (sin B))
14.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series349.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (* x (cos B)) (sin B))
134.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
46.0ms
(* x (cos B))
25.0ms
(/ 1 (sin B))

simplify47.3s

Counts
330 → 220
Calls
330 calls:
Slowest
760.0ms
(fma (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ 1 (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
503.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
476.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
475.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (/ (* x (cos B)) (sin B)) (/ (* x (cos B)) (sin B))) (* (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))))
451.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos B) (/ (sin B) x))
0.2b
(/ (sin B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
1373×times-frac
862×add-sqr-sqrt
842×*-un-lft-identity
832×add-cube-cbrt
572×prod-diff
105×div-inv
19×associate-/r*
15×add-exp-log
14×associate-/r/
13×add-cbrt-cube fma-neg
9×associate-/l* difference-of-squares
6×div-exp add-log-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num frac-2neg distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
4 → 750
Calls
4 calls:
Slowest
53.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
21.0ms
(/ (cos B) (/ (sin B) x))
15.0ms
(/ (sin B) x)
10.0ms
(/ 1 (sin B))

series348.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
134.0ms
(/ (cos B) (/ (sin B) x))
46.0ms
(/ (sin B) x)
27.0ms
(/ 1 (sin B))

simplify5.9m

Counts
1405 → 762
Calls
1405 calls:
Slowest
1.2s
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ (cos B) (cbrt (/ (sin B) x))) (/ 1 (* (cbrt (/ (sin B) x)) (cbrt (/ (sin B) x)))))))
1.1s
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (cos B) (/ (cbrt (sin B)) (sqrt x))) (/ 1 (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt x))))))
979.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ (sqrt (cos B)) (/ (sin B) (cbrt x))) (/ (sqrt (cos B)) (/ 1 (* (cbrt x) (cbrt x)))))))
933.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (cbrt (cos B)) (/ (sqrt (sin B)) (sqrt x))) (/ (* (cbrt (cos B)) (cbrt (cos B))) (/ (sqrt (sin B)) (sqrt x))))))
835.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ (cos B) (/ (sin B) (cbrt x))) (/ 1 (/ 1 (* (cbrt x) (cbrt x)))))))

prune10.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (/ (sin B) x) (cos B)))
0.2b
(/ (/ (sin B) x) (cos B))
0.2b
(/ (sin B) x)
0.1b
(/ 1 (sin B))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
486×times-frac
246×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
52×associate-/r*
36×add-exp-log
24×div-inv
22×add-cbrt-cube associate-/l*
21×div-exp
11×cbrt-undiv
6×pow1
4×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp insert-posit16 log1p-expm1-u add-log-exp
2×pow-flip inv-pow
1×associate-/r/ associate-/l/
Counts
4 → 340
Calls
4 calls:
Slowest
19.0ms
(/ 1 (sin B))
18.0ms
(/ 1 (/ (/ (sin B) x) (cos B)))
12.0ms
(/ (/ (sin B) x) (cos B))
8.0ms
(/ (sin B) x)

series358.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(/ 1 (/ (/ (sin B) x) (cos B)))
112.0ms
(/ (/ (sin B) x) (cos B))
51.0ms
(/ (sin B) x)
28.0ms
(/ 1 (sin B))

simplify49.1s

Counts
540 → 352
Calls
540 calls:
Slowest
659.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (/ 1 (* (cbrt x) (cbrt x))) (* (cbrt (cos B)) (cbrt (cos B)))))
615.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt x)) (* (cbrt (cos B)) (cbrt (cos B)))))
602.0ms
(log1p (/ 1 (/ (/ (sin B) x) (cos B))))
591.0ms
(/ (* (* 1 1) 1) (* (* (/ (/ (sin B) x) (cos B)) (/ (/ (sin B) x) (cos B))) (/ (/ (sin B) x) (cos B))))
555.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (/ (sqrt (sin B)) (* (cbrt x) (cbrt x))) (* (cbrt (cos B)) (cbrt (cos B)))))

prune4.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes582.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
3.6s1732×body1280valid
2.2s4897×body80valid
1.9s1393×body640valid
774.0ms380×body160valid
659.0ms733×body320valid