Details

Time bar (total: 8.0s)

sample26.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
7.0ms264×body80nan

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0217
1416
2696
3956
41256
51406
61426
71426

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.0b
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
95×add-sqr-sqrt *-un-lft-identity
67×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num associate-/l/
1×flip3-- div-sub associate-/r/ flip-- fma-udef
Counts
3 → 142
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
5.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
22.0ms
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series173.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
48.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
82.0ms
(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06271691
123791609
250021609

prune401.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)))
0.1b
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.1b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
0.2b
(/ (- (sqrt x) (sqrt 1.0)) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
839×times-frac
755×add-sqr-sqrt
580×*-un-lft-identity
519×sqrt-prod
348×add-cube-cbrt
203×associate-*r*
180×difference-of-squares
90×distribute-lft-out--
34×add-exp-log associate-*l* add-cbrt-cube
31×associate-/r*
26×distribute-lft-out
24×div-inv
20×associate-/l*
14×cbrt-undiv div-exp
12×unswap-sqr
6×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg clear-num
2×associate-/r/
1×frac-times flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 622
Calls
4 calls:
211.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)))
35.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
7.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
43.0ms
(/ (- (sqrt x) (sqrt 1.0)) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
460.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)))
241.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
102.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
319.0ms
(/ (- (sqrt x) (sqrt 1.0)) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) 6.0))

simplify140.0ms

Algorithm
egg-herbie
Counts
634 → 634
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0188912378
1500211852

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0)
0.0b
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
0.1b
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.1b
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
205×add-sqr-sqrt
197×*-un-lft-identity
195×sqrt-prod
170×times-frac
93×add-cube-cbrt
92×associate-*l*
52×difference-of-squares
34×add-exp-log add-cbrt-cube
26×distribute-lft-out distribute-lft-out--
14×associate-/l*
12×prod-exp associate-/r* cbrt-unprod
11×pow1
8×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ log1p-expm1-u div-inv associate-/l/ add-log-exp
3×unswap-sqr
2×frac-2neg clear-num *-commutative
1×frac-times flip3-- flip3-+ div-sub associate-*r/ flip-- flip-+
Counts
4 → 285
Calls
4 calls:
60.0ms
(* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0)
106.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
35.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
36.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
309.0ms
(* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0)
456.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
249.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
259.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify132.0ms

Algorithm
egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09154894
137764418
250034356

prune722.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
2×cbrt-div
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 56
Calls
4 calls:
8.0ms
(cbrt (- x 1.0))
1.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
1.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
1.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

series546.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(cbrt (- x 1.0))
143.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
149.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
145.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

simplify100.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0326571
1907524
23043505
35002499

prune320.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01918
11918

end0.0ms

sample676.0ms

Algorithm
intervals
Results
234.0ms8000×body80valid
199.0ms7948×body80nan