Details

Time bar (total: 3.4m)

sample370.0ms

Algorithm
intervals
Results
116.0ms57×body1280valid
49.0ms49×body640valid
35.0ms158×body80valid
16.0ms25×body320valid
4.0ms9×body160valid

simplify129.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
128.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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)))

rewrite204.0ms

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
157.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
14.0ms
(/ x (tan B))
11.0ms
(/ 1 (sin B))

series475.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
271.0ms
(/ x (tan B))
177.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
27.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
832.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
590.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
589.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
585.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
574.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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
32.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ 1 (sin B))
10.0ms
(/ x (tan B))

series303.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
146.0ms
(/ x (tan B))
142.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
14.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
678.0ms
(fma (- (/ (cbrt x) (cbrt (tan B)))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B))))))
615.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ (sqrt x) (cbrt (tan B))) (/ (sqrt x) (* (cbrt (tan B)) (cbrt (tan B)))))))
595.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
563.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
563.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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)))

rewrite72.0ms

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
30.0ms
(/ (* x (cos B)) (sin B))
23.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series315.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
115.0ms
(/ (* x (cos B)) (sin B))
57.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify41.6s

Counts
274 → 220
Calls
274 calls:
Slowest
753.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ (cos B) (cbrt (sin B))) (/ x (* (cbrt (sin B)) (cbrt (sin B)))))))
678.0ms
(fma (- (/ 1 (sin B))) (* x (cos B)) (* (/ 1 (sin B)) (* x (cos B))))
493.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
420.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
410.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (cos B) (cbrt (sin B))) (/ x (* (cbrt (sin B)) (cbrt (sin B)))))))

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos B))
0.3b
(cbrt (cos B))
0.3b
(cbrt (cos B))
0.2b
(* (cbrt (cos B)) (cbrt (cos B)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
20.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
2.0ms
(cbrt (cos B))
2.0ms
(cbrt (cos B))
2.0ms
(cbrt (cos B))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
162.0ms
(cbrt (cos B))
143.0ms
(cbrt (cos B))
138.0ms
(cbrt (cos B))

simplify1.6s

Counts
65 → 97
Calls
65 calls:
Slowest
401.0ms
(- 1 (+ (* 1/405 (pow B 6)) (* 1/3 (pow B 2))))
253.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
229.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
188.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
107.0ms
(* (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))) (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))))

prune955.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.9s1701×body1280valid
1.9s1462×body640valid
1.5s4890×body80valid
662.0ms729×body320valid
233.0ms361×body160valid