Details

Time bar (total: 1.8m)

sample136.0ms

Algorithm
intervals
Results
63.0ms240×body80nan
48.0ms256×body80valid

simplify250.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
250.0ms
(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))
0.4b
(* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))
0.2b
(* PI t)
0.2b
(* 5 (* v v))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
18×associate-*r/
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×*-un-lft-identity add-cube-cbrt
8×flip3-- sqrt-div associate-*r* associate-/r/ flip--
7×associate-*l* pow-prod-down
4×expm1-log1p-u frac-times cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ unswap-sqr associate-/l/
1×clear-num associate-/r* frac-2neg div-sub sqrt-prod div-inv
Counts
4 → 106
Calls
4 calls:
Slowest
151.0ms
(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))
56.0ms
(* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))
27.0ms
(* 5 (* v v))
11.0ms
(* PI t)

series926.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
606.0ms
(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))
248.0ms
(* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))
39.0ms
(* PI t)
32.0ms
(* 5 (* v v))

simplify14.1s

Counts
71 → 118
Calls
71 calls:
Slowest
1.5s
(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))
1.1s
(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (* (* (* PI PI) PI) (* (* t t) t)) (* (* (sqrt (* 2 (- 1 (* 3 (* v v))))) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (sqrt (* 2 (- 1 (* 3 (* v v))))))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))))
1.0s
(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))) (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v))))))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))))
1.0s
(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (* (* (* PI t) (* PI t)) (* PI t)) (* (* (sqrt (* 2 (- 1 (* 3 (* v v))))) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (sqrt (* 2 (- 1 (* 3 (* v v))))))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))))
431.0ms
(sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (/ 1 t) PI) (sqrt (fma -6 (* v v) 2)))
0.3b
(/ (/ 1 t) PI)
0.2b
(* 5 (* v v))
0.0b
(/ (- 1 (* 5 (* v v))) (- 1 (* v v)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
810×times-frac
395×add-sqr-sqrt
394×*-un-lft-identity
390×add-cube-cbrt
132×sqrt-prod
59×associate-/l*
35×add-exp-log div-inv
25×add-cbrt-cube
18×div-exp
14×associate-/r*
10×cbrt-undiv
9×pow1
8×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rec-exp flip3-- 1-exp associate-/r/ flip--
1×div-sub associate-*r* *-commutative unswap-sqr
Counts
4 → 469
Calls
4 calls:
Slowest
30.0ms
(/ (- 1 (* 5 (* v v))) (- 1 (* v v)))
27.0ms
(* 5 (* v v))
13.0ms
(/ (/ (/ 1 t) PI) (sqrt (fma -6 (* v v) 2)))
8.0ms
(/ (/ 1 t) PI)

series403.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
218.0ms
(/ (/ (/ 1 t) PI) (sqrt (fma -6 (* v v) 2)))
100.0ms
(/ (- 1 (* 5 (* v v))) (- 1 (* v v)))
48.0ms
(/ (/ 1 t) PI)
37.0ms
(* 5 (* v v))

simplify1.0m

Counts
736 → 481
Calls
736 calls:
Slowest
999.0ms
(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v))))
699.0ms
(/ (/ (/ (* (cbrt 1) (cbrt 1)) (sqrt t)) (* (cbrt PI) (cbrt PI))) (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt (sqrt (fma -6 (* v v) 2)))))
571.0ms
(/ (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt t) (cbrt t))) (* (cbrt PI) (cbrt PI))) 1)
468.0ms
(/ (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt t) (cbrt t))) 1) (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt (sqrt (fma -6 (* v v) 2)))))
465.0ms
(/ (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt t) (cbrt t))) (* (cbrt PI) (cbrt PI))) (sqrt 1))

prune6.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(/ 1 (sqrt (fma (* v v) -6 2)))
0.5b
(/ (/ 1 (sqrt (fma (* v v) -6 2))) (* t (sqrt PI)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
49×add-sqr-sqrt
47×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
30×add-exp-log
25×associate-/l*
18×add-cbrt-cube
14×div-exp
8×pow1
7×cbrt-undiv associate-/r*
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
3×rec-exp sqrt-pow1 pow1/2 1-exp pow-flip
2×rem-sqrt-square clear-num frac-2neg cbrt-unprod
1×inv-pow associate-/l/
Counts
4 → 151
Calls
4 calls:
Slowest
25.0ms
(/ (/ 1 (sqrt (fma (* v v) -6 2))) (* t (sqrt PI)))
10.0ms
(/ 1 (sqrt (fma (* v v) -6 2)))
3.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series724.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
566.0ms
(/ (/ 1 (sqrt (fma (* v v) -6 2))) (* t (sqrt PI)))
157.0ms
(/ 1 (sqrt (fma (* v v) -6 2)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify10.5s

Counts
143 → 159
Calls
143 calls:
Slowest
470.0ms
(- (* 1/36 (/ 1 (* t (* (pow v 3) (* (sqrt (/ -1/6 PI)) PI))))) (/ (sqrt (/ -1/6 PI)) (* t v)))
428.0ms
(- (+ (* 9/4 (* (/ (pow v 4) (* t (sqrt 1/2))) (sqrt (/ 1 PI)))) (+ (* (/ (sqrt 1/2) t) (sqrt (/ 1 PI))) (* 3/4 (* (/ (pow v 2) (* t (sqrt 1/2))) (sqrt (/ 1 PI)))))) (* 9/32 (* (/ (pow v 4) (* t (pow (sqrt 1/2) 3))) (sqrt (/ 1 PI)))))
389.0ms
(- (+ (sqrt 1/2) (+ (* 9/4 (/ (pow v 4) (sqrt 1/2))) (* 3/4 (/ (pow v 2) (sqrt 1/2))))) (* 9/32 (/ (pow v 4) (pow (sqrt 1/2) 3))))
331.0ms
(/ (* (* (/ 1 (sqrt (fma (* v v) -6 2))) (/ 1 (sqrt (fma (* v v) -6 2)))) (/ 1 (sqrt (fma (* v v) -6 2)))) (* (* (* t t) t) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))))
271.0ms
(- (- (log 1) (log (sqrt (fma (* v v) -6 2)))) (+ (log t) (log (sqrt PI))))

prune2.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
24×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×associate-*l*
6×pow1 associate-*r* add-exp-log unswap-sqr
5×pow1/3 sqrt-prod
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down
1×prod-exp *-commutative cbrt-unprod
Counts
4 → 78
Calls
4 calls:
Slowest
24.0ms
(* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI))
2.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series361.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
361.0ms
(* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify2.7s

Counts
45 → 84
Calls
45 calls:
Slowest
444.0ms
(* (* (/ 1 (* (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI)) (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI)))) (/ (/ (/ 1 t) (cbrt PI)) (cbrt (sqrt (fma -6 (* v v) 2))))) (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))
383.0ms
(* (* (/ 1 (* (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI)) (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI)))) (/ (/ (/ 1 t) (cbrt PI)) (cbrt (sqrt (fma -6 (* v v) 2))))) (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))
340.0ms
(* (* (/ 1 (* (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI)) (* (cbrt (sqrt (fma -6 (* v v) 2))) (cbrt PI)))) (/ (/ (/ 1 t) (cbrt PI)) (cbrt (sqrt (fma -6 (* v v) 2))))) (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))
257.0ms
(- (* (exp (* 1/6 (- (log -6) (* 2 (log (/ -1 v)))))) (pow PI 1/3)) (+ (* 5/648 (* (/ (exp (* 1/6 (- (log -6) (* 2 (log (/ -1 v)))))) (pow v 4)) (pow PI 1/3))) (* 1/18 (* (/ (exp (* 1/6 (- (log -6) (* 2 (log (/ -1 v)))))) (pow v 2)) (pow PI 1/3)))))
243.0ms
(- (* (pow PI 1/3) (exp (* 1/6 (- (log -6) (* 2 (log (/ 1 v))))))) (+ (* 5/648 (* (/ (exp (* 1/6 (- (log -6) (* 2 (log (/ 1 v)))))) (pow v 4)) (pow PI 1/3))) (* 1/18 (* (/ (exp (* 1/6 (- (log -6) (* 2 (log (/ 1 v)))))) (pow v 2)) (pow PI 1/3)))))

prune1.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes289.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch6.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.9s8050×body80nan
1.4s8000×body80valid