Details

Time bar (total: 30.4s)

sample195.0ms

Algorithm
intervals
Results
44.0ms14×body320nan
22.0ms344×body80nan
16.0ms52×body640valid
11.0ms152×body80valid
8.0ms23×body1280valid
5.0ms21×body640nan
5.0ms16×body1280nan
4.0ms20×body320valid
1.0ms9×body160valid
1.0ms6×body160nan

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
01827
14126
210026
322426
449726
594126
6155526
7330526
done500126

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize24.0ms

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)
14.4b
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
19.4b
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite140.0ms

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:
54.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
16.0ms
(* (sqrt 2.0) t)
28.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
35.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.6s

Counts
4 → 12
Calls
4 calls:
685.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
75.0ms
(* (sqrt 2.0) t)
291.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
560.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify4.0s

Counts
100 → 100
Iterations

Useful iterations: 3 (2.2s)

IterNodesCost
01552445
13452250
211952062
349932025
done50002025

prune533.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 28.5b

localize44.0ms

Local error

Found 4 expressions with local error:

3.0b
(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
7.3b
(/ (pow l 2) x)
9.0b
(/ (pow t 2) x)
25.5b
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite27.0ms

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 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
9.0ms
(/ (pow l 2) x)
10.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series597.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
26.0ms
(/ (pow l 2) x)
23.0ms
(/ (pow t 2) x)
459.0ms
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.5s

Counts
139 → 139
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02171761
13761614
29121411
331821411
done50001410

prune879.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.0b
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
9.0b
(/ (pow t 2) x)
25.5b
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
8×add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-*r* associate-/r*
2×unswap-sqr
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
4 → 100
Calls
4 calls:
11.0ms
(* (sqrt 2.0) t)
0.0ms
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
10.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sqrt 2.0) t)
109.0ms
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
34.0ms
(/ (pow t 2) x)
223.0ms
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

simplify3.6s

Counts
112 → 112
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01861472
13521329
29731189
337681184
done50001183

prune593.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma t t (* (fabs l) (/ (fabs l) x)))
3.0b
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
9.0b
(/ (pow t 2) x)
25.5b
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
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×div-exp associate-/r* sqrt-prod
2×fma-udef
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
0.0ms
(fma t t (* (fabs l) (/ (fabs l) x)))
0.0ms
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
9.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(fma t t (* (fabs l) (/ (fabs l) x)))
94.0ms
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
20.0ms
(/ (pow t 2) x)
223.0ms
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

Counts
98 → 98
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01691458
13151314
28311164
331011160
done50011159

prune603.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

regimes430.0ms

Accuracy

78.8% (5.0b remaining)

Error of 8.9b against oracle of 3.9b and baseline of 27.5b

bsearch446.0ms

Steps
ItersRangePoint
10
3.2765607520744054e+111
2.9128648643875498e+128
2.5553097889102982e+120
9
-1.2813900032142045e+106
-3.166552929383693e+99
-4.318745676503489e+101

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03577
14277
done4277

end0.0ms

sample6.1s

Algorithm
intervals
Results
1.8s9904×body80nan
849.0ms5136×body80valid
664.0ms617×body320valid
565.0ms1034×body640valid
398.0ms844×body1280valid
340.0ms626×body1280nan
306.0ms614×body640nan
87.0ms313×body320nan
71.0ms369×body160valid
69.0ms184×body160nan