Details

Time bar (total: 7.7m)

sample238.0ms

Algorithm
intervals
Results
84.0ms54×body1280valid
77.0ms55×body640valid
40.0ms162×body80valid
15.0ms19×body320valid
5.0ms9×body160valid

simplify132.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
132.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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)))

rewrite65.0ms

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
36.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ 1 (sin B))
10.0ms
(/ x (tan B))

series284.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
136.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
131.0ms
(/ x (tan B))
17.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
610.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
595.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
595.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
586.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
569.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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
27.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
13.0ms
(/ 1 (/ (tan B) x))
7.0ms
(/ 1 (sin B))
6.0ms
(/ (tan B) x)

series344.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
107.0ms
(/ 1 (/ (tan B) x))
80.0ms
(/ (tan B) x)
17.0ms
(/ 1 (sin B))

simplify5.4m

Counts
1362 → 779
Calls
1362 calls:
Slowest
1.2s
(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))))))
952.0ms
(fma (- (/ (sqrt 1) (/ (tan B) (sqrt x)))) (/ (sqrt 1) (/ 1 (sqrt x))) (* (/ (sqrt 1) (/ (tan B) (sqrt x))) (/ (sqrt 1) (/ 1 (sqrt x)))))
923.0ms
(fma (- (/ (cbrt 1) (/ (tan B) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt x))) (* (/ (cbrt 1) (/ (tan B) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt x)))))
751.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ 1 (/ (tan B) (sqrt x))) (/ 1 (/ 1 (sqrt x))))))
739.0ms
(fma (- (/ (cbrt 1) (/ (tan B) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt x))) (* (/ (cbrt 1) (/ (tan B) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt x)))))

prune9.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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
32.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
23.0ms
(/ (* x (cos B)) (sin B))
10.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
151.0ms
(/ (* x (cos B)) (sin B))
64.0ms
(* x (cos B))
19.0ms
(/ 1 (sin B))

simplify42.1s

Counts
274 → 220
Calls
274 calls:
Slowest
811.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (* x (cos B)) (sin B)) 1)))
554.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
461.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
434.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
410.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv flip-- unswap-sqr
Counts
2 → 54
Calls
2 calls:
Slowest
12.0ms
(/ (- 1 (* x (cos B))) (sin B))
8.0ms
(* x (cos B))

series155.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
89.0ms
(/ (- 1 (* x (cos B))) (sin B))
66.0ms
(* x (cos B))

simplify1.9s

Counts
44 → 60
Calls
44 calls:
Slowest
356.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
245.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
204.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
95.0ms
(/ (- 1 (* x (cos B))) (cbrt (sin B)))
85.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune529.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes91.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.3s1763×body1280valid
2.5s1475×body640valid
1.3s4870×body80valid
549.0ms703×body320valid
164.0ms350×body160valid