Details

Time bar (total: 6.7s)

sample29.0ms

Algorithm
intervals
Results
14.0ms84×body1280valid
4.0ms143×body80valid
3.0ms20×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1266
2336
3356
4416
5446
6446

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(hypot 1.0 x)
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.7b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-sqr-sqrt
13×add-cube-cbrt
12×prod-diff
8×add-log-exp
7×pow1
4×add-exp-log expm1-log1p-u sqrt-prod add-cbrt-cube log1p-expm1-u
3×fma-def fma-neg
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative sub-neg hypot-udef flip3-- pow1/2 diff-log pow-prod-down sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 73
Calls
4 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0ms
(hypot 1.0 x)
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
65.0ms
(hypot 1.0 x)
278.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
370.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04961013
11734765
25001762

prune237.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(hypot 1.0 x)
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
4×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
2×hypot-udef sqrt-pow1 sqrt-div associate-*r/
1×flip3-+ pow1/2 pow-prod-down sqrt-prod flip-+ fma-udef
Counts
4 → 45
Calls
4 calls:
1.0ms
(hypot 1.0 x)
1.0ms
(hypot 1.0 x)
11.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(hypot 1.0 x)
57.0ms
(hypot 1.0 x)
286.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
152.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0353405
11227375
25001366

prune244.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (hypot 1.0 x))
0.3b
(cbrt (hypot 1.0 x))
0.3b
(cbrt (hypot 1.0 x))
0.9b
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x)))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (hypot 1.0 x))
1.0ms
(cbrt (hypot 1.0 x))
1.0ms
(cbrt (hypot 1.0 x))
1.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x)))))))

series910.0ms

Counts
4 → 12
Calls
4 calls:
255.0ms
(cbrt (hypot 1.0 x))
247.0ms
(cbrt (hypot 1.0 x))
251.0ms
(cbrt (hypot 1.0 x))
157.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x)))))))

simplify92.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0238486
1754435
23245420
35002415

prune284.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b
(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b
(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2b
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
22×add-sqr-sqrt
18×associate-*r/
16×cbrt-div sqrt-div
14×add-cube-cbrt *-un-lft-identity
11×pow1
8×flip3-+ pow1/3 flip-+
7×swap-sqr associate-*r* associate-*l*
6×add-exp-log sqrt-prod
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 95
Calls
4 calls:
11.0ms
(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms
(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms
(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
574.0ms
(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
554.0ms
(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
572.0ms
(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
153.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05081607
119691496
250011419

prune419.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 14.3b

bsearch1.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05242
15642
26142
36242
46242

end0.0ms

sample817.0ms

Algorithm
intervals
Results
475.0ms2888×body1280valid
122.0ms4085×body80valid
77.0ms604×body640valid
24.0ms279×body320valid
8.0ms144×body160valid