Details

Time bar (total: 14.2s)

sample85.0ms

Algorithm
intervals
Results
27.0ms375×body80nan
8.0ms167×body80valid
8.0ms33×body1280valid
5.0ms28×body640valid
5.0ms21×body1280nan
3.0ms14×body640nan
2.0ms16×body320nan
2.0ms12×body320valid
2.0ms16×body160valid
1.0ms7×body160nan

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01827
14126
29426
321426
443326
583426
6133926
7224226
8493126
done500026

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.4b
(* (sqrt 2.0) t)
14.8b
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
20.6b
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
18.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
8.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
17.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.0s

Counts
4 → 12
Calls
4 calls:
446.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
41.0ms
(* (sqrt 2.0) t)
199.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
318.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify561.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
01552445
13482250
212782067
done50002067

prune363.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 30.7b

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b
(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
0.0ms
(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow l 2) x)
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
21.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
259.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify568.0ms

Counts
139 → 139
Iterations

Useful iterations: 2 (168.0ms)

IterNodesCost
02181816
13761665
212931462
done50001462

prune489.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
3.8b
(fma 2.0 (* t t) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
77×times-frac
56×unpow-prod-down
46×add-cube-cbrt *-un-lft-identity
37×associate-*r*
35×add-exp-log
24×unswap-sqr
22×cbrt-prod
18×sqr-pow
12×div-exp prod-exp
11×add-cbrt-cube unpow2
10×associate-*l*
8×pow-to-exp pow-exp associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* sqrt-prod
2×cbrt-undiv cbrt-unprod div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num *-commutative fma-udef
Counts
4 → 172
Calls
4 calls:
26.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
0.0ms
(fma 2.0 (* t t) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
90.0ms
(fma 2.0 (* t t) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
288.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify1.1s

Counts
184 → 184
Iterations

Useful iterations: 2 (373.0ms)

IterNodesCost
03063146
17012855
226142365
done50012365

prune699.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize30.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l))))
3.8b
(fma 2.0 (* t t) (fma 2.0 (* (/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l)))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l)))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
69×add-sqr-sqrt
68×add-cube-cbrt *-un-lft-identity
60×unpow-prod-down
33×add-exp-log
24×cbrt-prod
18×div-exp associate-/l*
13×add-cbrt-cube div-inv
12×sqr-pow
10×associate-/r*
6×cbrt-undiv
5×pow1
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u unpow2 add-log-exp
3×prod-exp sqrt-prod
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ cbrt-unprod fma-udef
Counts
4 → 188
Calls
4 calls:
13.0ms
(/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l))))
0.0ms
(fma 2.0 (* t t) (fma 2.0 (* (/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l)))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l)))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l))))
129.0ms
(fma 2.0 (* t t) (fma 2.0 (* (/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l)))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
278.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ (pow (cbrt l) 4) (/ (* (cbrt x) (cbrt x)) (fabs (cbrt l)))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify997.0ms

Counts
200 → 200
Iterations

Useful iterations: done (990.0ms)

IterNodesCost
04064702
18704386
230843963
done50013962

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes380.0ms

Accuracy

65.6% (8.4b remaining)

Error of 12.3b against oracle of 3.9b and baseline of 28.3b

bsearch173.0ms

Steps
ItersRangePoint
10
3.953010055594803e+65
5.675578072705738e+76
1.771713359426446e+69
4
-7.071793886822642e-265
-4.409591838871608e-265
-6.971334801643659e-265

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04186
14686
done4686

end0.0ms

sample2.0s

Algorithm
intervals
Results
459.0ms9913×body80nan
259.0ms5098×body80valid
207.0ms828×body1280valid
200.0ms1032×body640valid
133.0ms581×body1280nan
111.0ms614×body640nan
92.0ms666×body320valid
48.0ms350×body320nan
35.0ms376×body160valid
16.0ms178×body160nan