Details

Time bar (total: 23.4s)

sample603.0ms

Algorithm
intervals
Results
154.0ms154×body80valid
75.0ms323×body80nan
73.0ms13×body1280nan
49.0ms34×body640nan
23.0ms32×body1280valid
20.0ms41×body640valid
8.0ms20×body320valid
5.0ms11×body320nan
2.0ms9×body160valid
1.0ms4×body160nan

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
01827
14126
210026
323226
452626
5109226
6198526
7470326
done500026

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l)))))
0.5b
(* (sqrt 2.0) t)
13.9b
(fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l)))
18.3b
(sqrt (fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* times-frac associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r*
2×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative fma-udef div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
19.0ms
(/ (* (sqrt 2.0) t) (sqrt (fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l)))))
16.0ms
(* (sqrt 2.0) t)
1.0ms
(fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l)))
6.0ms
(sqrt (fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l))))

series2.5s

Counts
4 → 12
Calls
4 calls:
588.0ms
(/ (* (sqrt 2.0) t) (sqrt (fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l)))))
61.0ms
(* (sqrt 2.0) t)
235.0ms
(fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l)))
1.6s
(sqrt (fma (/ (+ x 1.0) (- x 1.0)) (fma l l (* 2.0 (* t t))) (- (* l l))))

simplify1.5s

Counts
90 → 90
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01522115
13671939
219861767
done50011761

prune829.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.9b

localize34.0ms

Local error

Found 4 expressions with local error:

3.4b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
6.6b
(/ (pow l 2) x)
7.3b
(/ (pow t 2) x)
28.2b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×add-cbrt-cube unpow2 sqr-pow
6×associate-/r* div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
0.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
7.0ms
(/ (pow l 2) x)
7.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
20.0ms
(/ (pow l 2) x)
25.0ms
(/ (pow t 2) x)
259.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify1.2s

Counts
139 → 139
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02141767
13921621
215901427
done50001420

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize51.0ms

Local error

Found 4 expressions with local error:

1.3b
(fma t t (/ l (/ x l)))
3.4b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l)))))
7.3b
(/ (pow t 2) x)
28.2b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
12×unpow-prod-down
9×add-exp-log
8×associate-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×associate-/r* div-exp sqrt-prod
2×fma-udef
1×pow-to-exp cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-exp div-inv
Counts
4 → 86
Calls
4 calls:
0.0ms
(fma t t (/ l (/ x l)))
0.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l)))))
7.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l))))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(fma t t (/ l (/ x l)))
108.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l)))))
21.0ms
(/ (pow t 2) x)
248.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l))))))

simplify643.0ms

Counts
98 → 98
Iterations

Useful iterations: done (636.0ms)

IterNodesCost
01561364
12871266
211441124
done50011117

prune768.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize47.0ms

Local error

Found 4 expressions with local error:

1.3b
(fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.4b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
7.3b
(/ (pow t 2) x)
28.2b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
12×unpow-prod-down
9×add-exp-log
8×associate-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×associate-/r* div-exp sqrt-prod
2×fma-udef
1×pow-to-exp cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-exp div-inv
Counts
4 → 86
Calls
4 calls:
1.0ms
(fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
1.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
14.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
134.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
29.0ms
(/ (pow t 2) x)
289.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify697.0ms

Counts
98 → 98
Iterations

Useful iterations: done (691.0ms)

IterNodesCost
01571658
12921546
211601369
done50011362

prune735.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

regimes642.0ms

Accuracy

74.9% (5.9b remaining)

Error of 9.9b against oracle of 4.0b and baseline of 27.6b

bsearch1.1s

Steps
ItersRangePoint
6
8.623848016624398e+24
9.25260478315882e+25
9.046331744575269e+25
9
5.484638728691009e-165
1.2245728681896357e-155
5.50990658974305e-162
9
1.1519454628559112e-253
1.131608625978812e-245
1.1078784155040597e-245
4
-2.096749817466635e-267
-1.3269116759083333e-267
-1.6506396057830864e-267
3
-1.0354862889270409e-218
-7.765673620927192e-219
-9.222092584370252e-219
7
-3.1546277032128373e+125
-9.219607530101453e+123
-1.4587104671199554e+125

simplify20.0ms

Iterations

Useful iterations: done (19.0ms)

IterNodesCost
064238
177199
280177
383177
done83176

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.7s9978×body80nan
815.0ms5077×body80valid
613.0ms589×body640nan
549.0ms856×body1280valid
423.0ms601×body1280nan
399.0ms1084×body640valid
257.0ms620×body320valid
120.0ms363×body160valid
86.0ms329×body320nan
27.0ms161×body160nan