Details

Time bar (total: 10.6s)

sample156.0ms

Algorithm
intervals
Results
40.0ms295×body80nan
32.0ms163×body80valid
15.0ms33×body640valid
12.0ms21×body1280valid
11.0ms30×body320valid
10.0ms18×body1280nan
6.0ms15×body640nan
3.0ms9×body320nan
2.0ms9×body160valid
1.0ms6×body160nan

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize19.0ms

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)
13.1b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.9b
(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:
29.0ms
(/ (* (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))
24.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
414.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms
(* (sqrt 2.0) t)
209.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s
(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 (51.0ms)

IterNodesCost
04461291
122061177
250021172

prune363.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

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))))
4.5b
(/ (pow l 2) x)
9.3b
(/ (pow t 2) x)
27.7b
(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)
4.0ms
(/ (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)))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
268.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0377811
11351724
25001715

prune496.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
9.3b
(/ (pow t 2) x)
27.7b
(sqrt (fma 2.0 (pow t 2) (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:
5.0ms
(* (sqrt 2.0) t)
0.0ms
(fma 2.0 (pow t 2) (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 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series264.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (sqrt 2.0) t)
60.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
148.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0356740
11496654
25001649

prune431.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.8b
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
9.3b
(/ (pow t 2) x)
27.7b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×add-exp-log
17×pow1
12×unpow-prod-down add-cbrt-cube
8×pow-prod-down prod-exp cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-/r* sqrt-prod
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* pow-exp clear-num *-commutative fma-udef div-inv
Counts
4 → 100
Calls
4 calls:
21.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
5.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series272.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
56.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
149.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0407917
11622753
25001704

prune414.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.8b

regimes648.0ms

Accuracy

77.5% (5.5b remaining)

Error of 9.6b against oracle of 4.1b and baseline of 28.4b

bsearch274.0ms

Steps
ItersRangePoint
10
1.1469398243808202e+81
1.1762467128593058e+94
5.7232019252513384e+81
6
-1.3322015116014577e+144
-1.1133040860713562e+143
-5.019195104122993e+143

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05563
15563

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s10142×body80nan
755.0ms5157×body80valid
472.0ms844×body1280valid
431.0ms960×body640valid
327.0ms602×body1280nan
260.0ms597×body640nan
229.0ms653×body320valid
112.0ms319×body320nan
95.0ms386×body160valid
39.0ms158×body160nan