Details

Time bar (total: 5.9s)

sample30.0ms

Algorithm
intervals
Results
14.0ms89×body1280valid
4.0ms138×body80valid
2.0ms20×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: 11.6b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def fma-neg associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
8.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series840.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
102.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
102.0ms
(/ 1.0 (hypot 1.0 x))
369.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05331129
12036878
25001876

prune282.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative flip3-+ sum-log flip-+ fma-udef distribute-lft-out
Counts
4 → 85
Calls
4 calls:
4.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series835.0ms

Counts
4 → 12
Calls
4 calls:
482.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
99.0ms
(/ 1.0 (hypot 1.0 x))
100.0ms
(/ 1.0 (hypot 1.0 x))
154.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0430681
11662625
25001623

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
5×pow1
4×expm1-log1p-u exp-prod log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×log-pow fma-udef rem-exp-log
Counts
4 → 85
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series488.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ 1.0 (hypot 1.0 x))
97.0ms
(/ 1.0 (hypot 1.0 x))
146.0ms
(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
144.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 3 (144.0ms)

IterNodesCost
0273648
1913592
24559571
35001565

prune363.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.1b
(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
9×add-exp-log
8×add-cbrt-cube
6×pow1 associate-/r* associate-/l*
4×expm1-log1p-u pow-unpow log1p-expm1-u add-log-exp
3×unpow-prod-up unpow-prod-down log-prod
2×cbrt-undiv frac-2neg div-exp pow-exp clear-num div-inv
1×pow-to-exp e-exp-1 pow-pow log-pow fma-udef sqr-pow
Counts
4 → 92
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series771.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1.0 (hypot 1.0 x))
99.0ms
(/ 1.0 (hypot 1.0 x))
413.0ms
(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
152.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0359776
11368725
25002716

prune383.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes350.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04437
14437

end0.0ms

sample793.0ms

Algorithm
intervals
Results
452.0ms2835×body1280valid
117.0ms4065×body80valid
80.0ms647×body640valid
31.0ms305×body320valid
11.0ms148×body160valid