Details

Time bar (total: 1.1m)

sample268.0ms

Algorithm
intervals
Results
124.0ms114×body2560valid
50.0ms63×body1280valid
30.0ms259×body80nan
22.0ms38×body640valid
19.0ms16×body320valid
4.0ms14×body160valid
2.0ms11×body80valid

simplify198.0ms

Calls
1 calls:
Slowest
198.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 2 expressions with local error:

0.6b
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b
(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
17×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
8×difference-of-squares
6×associate-/r*
4×add-cbrt-cube difference-of-sqr-1 add-exp-log
3×associate-/l*
2×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin cbrt-undiv clear-num frac-2neg flip3-- div-exp div-inv flip--
Calls
2 calls:
Slowest
20.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
1.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series70.0ms

Calls
2 calls:
Slowest
65.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
5.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify4.6s

Calls
54 calls:
Slowest
254.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
240.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
199.0ms
(/ (cbrt (fma -5 (* v v) 1)) (sqrt (- (* v v) 1)))
184.0ms
(/ (sqrt (fma -5 (* v v) 1)) (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))))
171.0ms
(+ (* (* v v) (* v v)) (+ (* 1 1) (* (* v v) 1)))

prune428.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.6b
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))
0.0b
(/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
77×add-sqr-sqrt *-un-lft-identity
65×add-cube-cbrt
24×difference-of-squares
22×associate-/r*
13×add-exp-log
12×difference-of-sqr-1
7×add-cbrt-cube div-exp
5×div-inv
3×pow1 cbrt-undiv associate-/l*
2×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin clear-num frac-2neg associate-/r/ pow-flip inv-pow
Calls
2 calls:
Slowest
13.0ms
(/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))
1.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

series95.0ms

Calls
2 calls:
Slowest
90.0ms
(/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))
5.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

simplify27.8s

Calls
170 calls:
Slowest
1.0s
(/ (* (* 1 1) 1) (* (* (/ (- (* v v) 1) (fma -5 (* v v) 1)) (/ (- (* v v) 1) (fma -5 (* v v) 1))) (/ (- (* v v) 1) (fma -5 (* v v) 1))))
802.0ms
(/ (sqrt 1) (/ (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))) (* (cbrt (fma -5 (* v v) 1)) (cbrt (fma -5 (* v v) 1)))))
528.0ms
(/ (sqrt 1) (/ (- (* v v) 1) (fma -5 (* v v) 1)))
501.0ms
(/ (cbrt 1) (/ (- (* v v) 1) (fma -5 (* v v) 1)))
469.0ms
(/ (sqrt 1) (/ (- (* v v) 1) (fma -5 (* v v) 1)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.6b
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
0.0b
(fma (* v v) (* v v) (* v v))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin fma-udef
Calls
2 calls:
Slowest
1.0ms
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))
0.0ms
(fma (* v v) (* v v) (* v v))

series166.0ms

Calls
2 calls:
Slowest
160.0ms
(fma (* v v) (* v v) (* v v))
6.0ms
(acos (fma (fma (* v v) (* v v) (* v v)) 4 -1))

simplify265.0ms

Calls
6 calls:
Slowest
81.0ms
(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
57.0ms
(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
50.0ms
(acos (fma (fma (pow v 2) (pow v 2) (pow v 2)) 4 -1))
25.0ms
(+ (pow v 4) (pow v 2))
25.0ms
(+ (pow v 4) (pow v 2))

prune265.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))))
1.0b
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
1.0b
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
0.6b
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
16.0ms
(* (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))))
2.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
2.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
1.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

series48.0ms

Calls
4 calls:
Slowest
23.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
14.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
7.0ms
(* (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))))
3.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

simplify24.1s

Calls
82 calls:
Slowest
825.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))
478.0ms
(* (sqrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))) (sqrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))))
452.0ms
(* (* (* (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))) (* (* (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))))
448.0ms
(sqrt (* (cbrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (cbrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))))
446.0ms
(* (sqrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))) (sqrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))))

prune808.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

regimes115.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
3.6s3093×body2560valid
1.8s2418×body1280valid
981.0ms8122×body80nan
709.0ms1259×body640valid
268.0ms631×body320valid
129.0ms405×body160valid
26.0ms194×body80valid