Details

Time bar (total: 1.4m)

sample209.0ms

Algorithm
intervals
Results
95.0ms88×body2560valid
48.0ms79×body1280valid
22.0ms270×body80nan
20.0ms47×body640valid
6.0ms18×body320valid
3.0ms14×body160valid
1.0ms10×body80valid

simplify178.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
178.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b
(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite13.0ms

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--
Counts
2 → 55
Calls
2 calls:
Slowest
11.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
1.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series90.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
84.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
5.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify5.0s

Counts
54 → 61
Calls
54 calls:
Slowest
410.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
334.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
202.0ms
(- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1)
192.0ms
(/ (* (cbrt (fma -5 (* v v) 1)) (cbrt (fma -5 (* v v) 1))) (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))))
181.0ms
(- (log (fma -5 (* v v) 1)) (log (- (* v v) 1)))

prune526.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
0.0b
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
0.0b
(/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))
0.0b
(sqrt (fma -5 (* v v) 1))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
112×times-frac
77×*-un-lft-identity
62×sqrt-prod
58×add-cube-cbrt
42×associate-*r*
26×difference-of-squares
23×add-exp-log
22×associate-*l*
18×add-cbrt-cube
15×unswap-sqr
13×difference-of-sqr-1
8×div-exp
7×pow1
6×associate-/r* prod-exp associate-/l*
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×flip3-- 1-exp flip--
1×acos-asin frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 196
Calls
4 calls:
Slowest
46.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
25.0ms
(/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))
2.0ms
(sqrt (fma -5 (* v v) 1))
1.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))
87.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
80.0ms
(sqrt (fma -5 (* v v) 1))
6.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))

simplify25.0s

Counts
212 → 208
Calls
212 calls:
Slowest
582.0ms
(/ 1 (sqrt (- (* v v) 1)))
512.0ms
(- (+ (* (sqrt -5) v) (* 1/2 (/ 1 (* (sqrt -5) v)))) (* 1/8 (/ 1 (* (pow (sqrt -5) 3) (pow v 3)))))
454.0ms
(- 1 (+ (* 25/8 (pow v 4)) (* 5/2 (pow v 2))))
399.0ms
(- (* 1/8 (/ 1 (* (pow (sqrt -5) 3) (pow v 3)))) (+ (* (sqrt -5) v) (* 1/2 (/ 1 (* (sqrt -5) v)))))
376.0ms
(+ (- (log (sqrt (fma -5 (* v v) 1))) 0) (log (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
0.0b
(exp (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
0.0b
(log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))
0.0b
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
76×times-frac
51×*-un-lft-identity
42×associate-*r*
39×add-cube-cbrt
38×sqrt-prod
22×associate-*l* add-exp-log
16×add-cbrt-cube
15×unswap-sqr
12×difference-of-squares
8×pow1
7×div-exp
6×log-prod difference-of-sqr-1 prod-exp
4×expm1-log1p-u cbrt-undiv exp-prod cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×exp-sum
2×1-exp associate-/r/ log-pow div-inv
1×acos-asin frac-times flip3-- rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative flip-- rem-exp-log
Counts
4 → 148
Calls
4 calls:
Slowest
50.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
5.0ms
(exp (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
2.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
2.0ms
(log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))

series186.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
88.0ms
(log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))
3.0ms
(exp (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
3.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))

simplify18.2s

Counts
132 → 160
Calls
132 calls:
Slowest
473.0ms
(+ (- (log (sqrt (fma -5 (* v v) 1))) 0) (log (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
346.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
340.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
304.0ms
(exp (sqrt (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))))
300.0ms
(* (/ (* (* (sqrt (fma -5 (* v v) 1)) (sqrt (fma -5 (* v v) 1))) (sqrt (fma -5 (* v v) 1))) (* (* 1 1) 1)) (/ (* (* (sqrt (fma -5 (* v v) 1)) (sqrt (fma -5 (* v v) 1))) (sqrt (fma -5 (* v v) 1))) (* (* (- (* v v) 1) (- (* v v) 1)) (- (* v v) 1))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
0.0b
(pow E (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
0.0b
(log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))
0.0b
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
76×times-frac
52×*-un-lft-identity
42×associate-*r*
40×add-cube-cbrt
38×sqrt-prod
23×add-exp-log
22×associate-*l*
16×add-cbrt-cube
15×unswap-sqr
12×difference-of-squares
9×pow1
7×div-exp
6×log-prod difference-of-sqr-1 prod-exp
4×expm1-log1p-u cbrt-undiv pow-unpow cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×unpow-prod-up unpow-prod-down
2×1-exp pow-exp associate-/r/ log-pow div-inv
1×acos-asin frac-times pow-to-exp e-exp-1 pow-pow flip3-- rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative flip-- sqr-pow
Counts
4 → 155
Calls
4 calls:
Slowest
54.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
2.0ms
(pow E (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
1.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
1.0ms
(log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
385.0ms
(pow E (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
105.0ms
(log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))
100.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
10.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))

simplify20.6s

Counts
136 → 167
Calls
136 calls:
Slowest
677.0ms
(* (/ (sqrt (sqrt (fma -5 (* v v) 1))) (sqrt 1)) (/ (sqrt (sqrt (fma -5 (* v v) 1))) (sqrt (- (* v v) 1))))
434.0ms
(+ (- (log (sqrt (fma -5 (* v v) 1))) 0) (log (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
416.0ms
(pow E (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))
401.0ms
(pow E (log (sqrt (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))))))
387.0ms
(pow (sqrt E) (log (acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))))

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

regimes123.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
2.9s2996×body2560valid
1.9s2454×body1280valid
1.1s1301×body640valid
951.0ms8121×body80nan
278.0ms615×body320valid
101.0ms424×body160valid
88.0ms210×body80valid