Details

Time bar (total: 13.9s)

sample82.0ms

Algorithm
intervals
Results
15.0ms315×body80nan
13.0ms20×body1280nan
8.0ms168×body80valid
7.0ms36×body640valid
6.0ms23×body1280valid
4.0ms22×body640nan
2.0ms14×body320valid
1.0ms15×body160valid
1.0ms9×body320nan
1.0ms6×body160nan

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01827
14126
29426
321426
443326
583426
6133926
7224226
8493126
done500026

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b
(* (sqrt 2.0) t)
15.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite74.0ms

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--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
25.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
28.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
422.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms
(* (sqrt 2.0) t)
220.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify646.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
01792660
14442367
217892182
done50012182

prune379.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b
(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow t 2) x)
6.9b
(/ (pow l 2) x)
27.7b
(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

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 t 2) x)
8.0ms
(/ (pow l 2) x)
1.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series375.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
18.0ms
(/ (pow l 2) x)
268.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify627.0ms

Counts
139 → 139
Iterations

Useful iterations: 2 (174.0ms)

IterNodesCost
02181816
13761665
212931462
done50011462

prune494.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
5.6b
(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow t 2) x)
27.7b
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

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:
4.0ms
(* (sqrt 2.0) t)
0.0ms
(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sqrt 2.0) t)
56.0ms
(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
25.0ms
(/ (pow t 2) x)
144.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify580.0ms

Counts
112 → 112
Iterations

Useful iterations: done (577.0ms)

IterNodesCost
01861525
13551379
213251249
done50001248

prune435.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
5.6b
(fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow t 2) x)
27.7b
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt times-frac
23×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×cbrt-prod div-exp associate-/r* sqrt-prod
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow1/3 pow-exp clear-num fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (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 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt x)
86.0ms
(fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
20.0ms
(/ (pow t 2) x)
285.0ms
(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify459.0ms

Counts
101 → 101
Iterations

Useful iterations: done (450.0ms)

IterNodesCost
01701556
13091435
210501222
done50001172

prune406.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.2b

regimes428.0ms

Accuracy

75.6% (5.9b remaining)

Error of 9.8b against oracle of 3.8b and baseline of 28.1b

bsearch480.0ms

Steps
ItersRangePoint
9
8249416806277068.0
6.908956904862703e+24
6.769189022626266e+24
9
-5.149414502062706e-287
-6.479421214823862e-296
-5.07338813022938e-287
9
-1.9154334448410318e-177
-2.122947083583308e-184
-1.1776830540197237e-181
8
-7.474441928331378e+61
-1.7381937350890755e+58
-8.171560713962325e+60

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
049165
156165
done56165

end0.0ms

sample2.2s

Algorithm
intervals
Results
497.0ms10142×body80nan
288.0ms587×body1280nan
259.0ms5082×body80valid
229.0ms879×body1280valid
201.0ms994×body640valid
112.0ms590×body640nan
95.0ms649×body320valid
46.0ms316×body320nan
39.0ms396×body160valid
20.0ms217×body160nan