Details

Time bar (total: 16.8s)

sample76.0ms

Algorithm
intervals
Results
15.0ms310×body80nan
8.0ms164×body80valid
6.0ms26×body1280valid
6.0ms31×body640valid
4.0ms19×body1280nan
4.0ms20×body640nan
3.0ms20×body320valid
2.0ms11×body320nan
1.0ms15×body160valid
1.0ms6×body160nan

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
01827
14126
210026
322426
449726
594126
6155526
7330526
done500126

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.5b

localize28.0ms

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)
12.6b
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
20.2b
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite104.0ms

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:
38.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
13.0ms
(* (sqrt 2.0) t)
19.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
31.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.1s

Counts
4 → 12
Calls
4 calls:
483.0ms
(/ (* (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)
212.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
340.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify2.3s

Counts
100 → 100
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01552445
13452250
211952062
349932025
done50002025

prune354.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 32.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b
(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
5.5b
(/ (pow l 2) x)
10.6b
(/ (pow t 2) x)
29.4b
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite26.0ms

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)))
8.0ms
(/ (pow l 2) x)
12.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
284.0ms
(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts
139 → 139
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02171761
13761614
29121411
331821411
done50001410

prune483.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma t t (* (fabs l) (/ (fabs l) x)))
3.8b
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
10.6b
(/ (pow t 2) x)
29.4b
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

rewrite13.0ms

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)))
8.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma t t (* (fabs l) (/ (fabs l) x)))
66.0ms
(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
20.0ms
(/ (pow t 2) x)
163.0ms
(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.4s

Counts
98 → 98
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01691458
13151314
28311164
331011160
done50011159

prune378.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
3.8b
(fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
10.6b
(/ (pow t 2) x)
29.4b
(sqrt (fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

rewrite12.0ms

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) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
0.0ms
(fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
8.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
87.0ms
(fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
19.0ms
(/ (pow t 2) x)
175.0ms
(sqrt (fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01701759
13211643
28491417
331151412
done50001267

prune380.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes294.0ms

Accuracy

74.2% (6.0b remaining)

Error of 10.2b against oracle of 4.2b and baseline of 27.5b

bsearch589.0ms

Steps
ItersRangePoint
9
1.465138554361753e+145
1.1978127855039438e+150
7.02010337201463e+147
4
8.850619474871086e-234
1.661088650457253e-233
1.4647836581094993e-233
9
4.423936161010146e-305
1.2565912718636627e-298
1.5390966172940503e-299
9
-1.1180435754089893e-220
-2.19452767567629e-228
-7.231141217156239e-225
7
-1.4908441577161578e-155
-6.389616883612984e-157
-6.492099203484522e-157
8
-2.831759546101662e+36
-1.2139019026724813e+32
-2.4046995940459546e+36

simplify13.0ms

Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
060198
170182
273158
376158
done76158

end0.0ms

sample2.2s

Algorithm
intervals
Results
490.0ms10161×body80nan
261.0ms5065×body80valid
207.0ms849×body1280valid
196.0ms1019×body640valid
142.0ms618×body1280nan
118.0ms632×body640nan
97.0ms679×body320valid
47.0ms349×body320nan
43.0ms388×body160valid
17.0ms184×body160nan