Details

Time bar (total: 16.5s)

sample119.0ms

Algorithm
intervals
Results
49.0ms256×body80valid
47.0ms271×body80nan

simplify92.0ms

Calls
1 calls:
Slowest
92.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

Local error

Found 3 expressions with local error:

1.0b
(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
1.0b
(/ (acos (/ (- g) h)) 3)
0.0b
(fma 2/3 PI (/ (acos (/ (- g) h)) 3))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-sub fma-udef
1×acos-asin cbrt-undiv acos-neg cos-sum clear-num frac-2neg div-exp distribute-frac-neg div-inv
Calls
3 calls:
Slowest
8.0ms
(/ (acos (/ (- g) h)) 3)
2.0ms
(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
0.0ms
(fma 2/3 PI (/ (acos (/ (- g) h)) 3))

series174.0ms

Calls
3 calls:
Slowest
121.0ms
(cos (fma 2/3 PI (/ (acos (/ (- g) h)) 3)))
41.0ms
(fma 2/3 PI (/ (acos (/ (- g) h)) 3))
11.0ms
(/ (acos (/ (- g) h)) 3)

simplify1.3s

Calls
36 calls:
Slowest
221.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
93.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
92.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
74.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
65.0ms
(* 1/3 (acos (* -1 (/ g h))))

prune686.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))
0.9b
(sqrt (acos (/ (- g) h)))
0.9b
(sqrt (acos (/ (- g) h)))
0.0b
(fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
1×cos-sum
Calls
4 calls:
Slowest
2.0ms
(cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))
2.0ms
(sqrt (acos (/ (- g) h)))
1.0ms
(sqrt (acos (/ (- g) h)))
0.0ms
(fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))

series223.0ms

Calls
4 calls:
Slowest
139.0ms
(cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))
52.0ms
(fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))
16.0ms
(sqrt (acos (/ (- g) h)))
16.0ms
(sqrt (acos (/ (- g) h)))

simplify852.0ms

Calls
23 calls:
Slowest
90.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
78.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
76.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
72.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
63.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))

prune885.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
1.0b
(cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))
1.0b
(expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))
0.9b
(sqrt (acos (/ (- g) h)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×expm1-log1p-u pow1 *-un-lft-identity add-cube-cbrt log1p-expm1-u
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×log1p-expm1
1×rem-sqrt-square cos-sum log1p-udef expm1-log1p sqrt-pow1 pow1/2 fma-udef expm1-udef
Calls
4 calls:
Slowest
2.0ms
(cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))
1.0ms
(sqrt (acos (/ (- g) h)))
0.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
0.0ms
(expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))

series537.0ms

Calls
4 calls:
Slowest
205.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
197.0ms
(expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))
125.0ms
(cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))
10.0ms
(sqrt (acos (/ (- g) h)))

simplify996.0ms

Calls
21 calls:
Slowest
91.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
89.0ms
(- (exp (cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))) 1)
87.0ms
(- (exp (cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))) 1)
86.0ms
(- (exp (cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))) 1)
68.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune814.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (* (* (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))))
1.0b
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
1.0b
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
1.0b
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
23×add-sqr-sqrt
18×associate-*l*
11×*-un-lft-identity add-cube-cbrt
7×expm1-log1p-u unswap-sqr
6×associate-*r* log1p-expm1
4×pow1 add-cbrt-cube swap-sqr add-exp-log *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×log1p-udef
2×pow3 rem-cbrt-cube
1×pow1/3
Calls
4 calls:
Slowest
20.0ms
(cbrt (* (* (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))))
0.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
0.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
0.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))

series838.0ms

Calls
4 calls:
Slowest
230.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
208.0ms
(cbrt (* (* (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))))
201.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))
198.0ms
(log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))

simplify3.1s

Calls
48 calls:
Slowest
180.0ms
(cbrt (* (* (cbrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (cbrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))) (* (cbrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (cbrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))))))
130.0ms
(cbrt (sqrt (* (* (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))))
122.0ms
(cbrt (* (* (sqrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (sqrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))) (sqrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))))
117.0ms
(cbrt (* (* (sqrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (sqrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))) (sqrt (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))))
113.0ms
(cbrt (* (cbrt (* (* (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))))) (cbrt (* (* (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3)))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))) (log1p (expm1 (cos (fma 2/3 PI (* (sqrt (acos (/ (- g) h))) (/ (sqrt (acos (/ (- g) h))) 3))))))))))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes255.0ms

Accuracy

0% (0.0b remaining)

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

bsearch16.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.3s8000×body80valid
1.6s7848×body80nan