Details

Time bar (total: 14.8s)

sample52.0ms

Algorithm
intervals
Results
30.0ms93×body1280valid
9.0ms137×body80valid
4.0ms16×body640valid
1.0ms6×body320valid
0.0ms4×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: 12.1b

localize11.0ms

Local error

Found 1 expressions with local error:

1.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×prod-diff
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
3×fma-neg sqrt-prod add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
Counts
1 → 31
Calls
1 calls:
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series351.0ms

Counts
1 → 3
Calls
1 calls:
351.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify38.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295671
11040440
25001438

prune93.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube distribute-lft-out
3×associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ fma-udef div-inv
Counts
2 → 45
Calls
2 calls:
6.0ms
(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series1.5s

Counts
2 → 6
Calls
2 calls:
1.3s
(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
147.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06461221
130821119
250021108

prune195.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (exp (log (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b
(exp (log (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
24×times-frac
22×add-sqr-sqrt add-cube-cbrt
18×log-prod exp-sum
7×distribute-lft-out
6×associate-/l*
5×add-cbrt-cube
4×pow1 add-exp-log exp-prod associate-/r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×associate-/r/
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num log-pow flip-+ fma-udef div-inv rem-exp-log
Counts
3 → 77
Calls
3 calls:
8.0ms
(/ (exp (log (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms
(exp (log (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series1.5s

Counts
3 → 9
Calls
3 calls:
1.2s
(/ (exp (log (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
147.0ms
(exp (log (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
148.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify93.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06991881
131771718
250011658

prune287.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.1b
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
237×add-sqr-sqrt
168×prod-diff
167×*-un-lft-identity
157×unpow-prod-down cube-prod
117×add-cube-cbrt
80×difference-of-squares
75×times-frac
68×sqr-pow
28×cube-mult unpow3
26×sqrt-prod
25×associate-/l* distribute-lft-out--
12×fma-neg
7×pow1
6×add-exp-log add-cbrt-cube
5×difference-cubes add-log-exp
4×pow-pow
3×expm1-log1p-u pow-unpow associate-/r* log1p-expm1-u
2×cube-div flip3-- sqrt-pow1 sqrt-div associate-*r/ flip-- associate-/l/
1×cbrt-undiv pow-to-exp sub-neg frac-2neg flip3-+ pow1/2 diff-log div-sub div-exp pow-prod-down pow-exp clear-num sqrt-pow2 flip-+ div-inv rem-cube-cbrt
Counts
3 → 369
Calls
3 calls:
72.0ms
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
9.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
25.0ms
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series7.8s

Counts
3 → 9
Calls
3 calls:
5.9s
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
677.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2s
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify168.0ms

Algorithm
egg-herbie
Counts
378 → 378
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0232411810
1500110688

prune751.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes187.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 14.8b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04537
14837
25237
35337
45337

end0.0ms

sample1.5s

Algorithm
intervals
Results
928.0ms2842×body1280valid
249.0ms4044×body80valid
172.0ms659×body640valid
55.0ms297×body320valid
19.0ms158×body160valid