Details

Time bar (total: 31.8s)

sample225.0ms

Algorithm
intervals
Results
106.0ms114×body2560valid
52.0ms63×body1280valid
25.0ms259×body80nan
17.0ms38×body640valid
6.0ms16×body320valid
3.0ms14×body160valid
2.0ms11×body80valid

simplify539.0ms

Calls
1 calls:
Slowest
539.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize18.0ms

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))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-/r* 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
6.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
1.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series78.0ms

Calls
2 calls:
Slowest
74.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
3.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify3.8s

Calls
40 calls:
Slowest
217.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
201.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
177.0ms
(/ (cbrt (fma -5 (* v v) 1)) (cbrt (- (* v v) 1)))
175.0ms
(/ (sqrt (fma -5 (* v v) 1)) (sqrt (- (* v v) 1)))
174.0ms
(/ (sqrt (fma -5 (* v v) 1)) (sqrt (- (* v v) 1)))

prune414.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

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)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-/r*
12×times-frac
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×add-exp-log
3×pow1 difference-of-sqr-1
2×expm1-log1p-u rec-exp add-cbrt-cube insert-posit16 log1p-expm1-u div-inv add-log-exp
1×acos-asin clear-num frac-2neg div-exp associate-/r/ pow-flip inv-pow
Calls
2 calls:
Slowest
5.0ms
(/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))
1.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

series82.0ms

Calls
2 calls:
Slowest
77.0ms
(/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))
5.0ms
(acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))

simplify3.3s

Calls
24 calls:
Slowest
249.0ms
(cbrt (/ (- (* v v) 1) (fma -5 (* v v) 1)))
244.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
234.0ms
(sqrt (/ (- (* v v) 1) (fma -5 (* v v) 1)))
233.0ms
(/ (- (* v v) 1) (fma -5 (* v v) 1))
215.0ms
(/ (- (* v v) 1) (cbrt (fma -5 (* v v) 1)))

prune458.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin cbrt-undiv clear-num frac-2neg div-exp div-inv
Calls
2 calls:
Slowest
4.0ms
(/ (fma (* v v) -5 1) (fma v v -1))
1.0ms
(acos (/ (fma (* v v) -5 1) (fma v v -1)))

series99.0ms

Calls
2 calls:
Slowest
96.0ms
(/ (fma (* v v) -5 1) (fma v v -1))
3.0ms
(acos (/ (fma (* v v) -5 1) (fma v v -1)))

simplify2.7s

Calls
31 calls:
Slowest
477.0ms
(/ (* (* (fma (* v v) -5 1) (fma (* v v) -5 1)) (fma (* v v) -5 1)) (* (* (fma v v -1) (fma v v -1)) (fma v v -1)))
225.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
220.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
131.0ms
(/ (* (cbrt (fma (* v v) -5 1)) (cbrt (fma (* v v) -5 1))) (sqrt (fma v v -1)))
130.0ms
(/ (* (cbrt (fma (* v v) -5 1)) (cbrt (fma (* v v) -5 1))) (* (cbrt (fma v v -1)) (cbrt (fma v v -1))))

prune483.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize8.0ms

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))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
10×*-un-lft-identity add-cube-cbrt
9×pow1
6×add-cbrt-cube pow1/2 associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow-prod-down pow-prod-up
1×pow2 acos-asin rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))) (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))))
1.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
1.0ms
(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
25.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
15.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
6.0ms
(* (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))))

simplify11.0s

Calls
42 calls:
Slowest
475.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))
447.0ms
(* (* (* (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)))))))
446.0ms
(* (cbrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))) (cbrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))))
439.0ms
(cbrt (sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1))))))
420.0ms
(sqrt (acos (/ 1 (/ (- (* v v) 1) (fma -5 (* v v) 1)))))

prune849.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes96.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
3.0s3093×body2560valid
1.9s2418×body1280valid
1.3s8122×body80nan
673.0ms1259×body640valid
249.0ms631×body320valid
125.0ms405×body160valid
25.0ms194×body80valid