Details

Time bar (total: 9.1s)

sample87.0ms

Algorithm
intervals
Results
18.0ms375×body80nan
17.0ms167×body80valid
9.0ms33×body1280valid
5.0ms28×body640valid
5.0ms21×body1280nan
3.0ms14×body640nan
2.0ms16×body320nan
2.0ms12×body320valid
2.0ms16×body160valid
1.0ms7×body160nan

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

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

rewrite73.0ms

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:
24.0ms
(/ (* (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)
18.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
421.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms
(* (sqrt 2.0) t)
215.0ms
(- (* (/ (+ 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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04461290
122061177
250021172

prune348.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.7b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b
(fma 2.0 (pow t 2) (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 (pow t 2) (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 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
269.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0377811
11351724
25001715

prune475.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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:
29.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
0.0ms
(fma 2.0 (pow t 2) (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 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

series450.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
91.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x))))
24.0ms
(/ (pow t 2) x)
291.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07041652
133791419
250011377

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize31.0ms

Local error

Found 4 expressions with local error:

3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
3.9b
(/ (pow (cbrt l) 4) (cbrt x))
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
66×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
54×cbrt-prod unpow-prod-down
18×associate-/l*
14×add-exp-log
11×sqr-pow
9×associate-/r*
7×add-cbrt-cube
6×div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 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 → 168
Calls
4 calls:
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
7.0ms
(/ (pow (cbrt l) 4) (cbrt x))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
94.0ms
(/ (pow (cbrt l) 4) (cbrt x))
18.0ms
(/ (pow t 2) x)
285.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06091847
122771728
250011653

prune911.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes559.0ms

Accuracy

65.9% (8.4b remaining)

Error of 12.2b against oracle of 3.8b and baseline of 28.3b

bsearch193.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05967
15967

end0.0ms

sample2.0s

Algorithm
intervals
Results
462.0ms9913×body80nan
262.0ms5098×body80valid
203.0ms828×body1280valid
197.0ms1032×body640valid
136.0ms581×body1280nan
113.0ms614×body640nan
98.0ms666×body320valid
49.0ms350×body320nan
35.0ms376×body160valid
16.0ms178×body160nan