Details

Time bar (total: 3.5s)

sample31.0ms

Algorithm
intervals
Results
20.0ms268×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (* a c) (* b d))
25.8b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(+ (* a c) (* b d))
11.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series121.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(+ (* a c) (* b d))
82.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify82.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0231450
1847413
22851412
35003412

prune139.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* a c) (* b d))
16.4b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.4b
(sqrt (+ (* c c) (* d d)))
28.4b
(sqrt (+ (* c c) (* d d)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
2.0ms
(+ (* a c) (* b d))
12.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(sqrt (+ (* c c) (* d d)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a c) (* b d))
109.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
40.0ms
(sqrt (+ (* c c) (* d d)))
35.0ms
(sqrt (+ (* c c) (* d d)))

simplify81.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0273893
1868840
22693828
35001828

prune273.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ (* a c) (* b d))
0.7b
(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
25.2b
(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
55×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
7×flip3-+ flip-+
6×div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
3 → 126
Calls
3 calls:
2.0ms
(+ (* a c) (* b d))
14.0ms
(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
11.0ms
(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series228.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(+ (* a c) (* b d))
143.0ms
(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
52.0ms
(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify59.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04801744
122371592
250031505

prune251.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
16.4b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.4b
(sqrt (+ (* c c) (* d d)))
28.4b
(sqrt (+ (* c c) (* d d)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 160
Calls
4 calls:
48.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
12.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
108.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
36.0ms
(sqrt (+ (* c c) (* d d)))
43.0ms
(sqrt (+ (* c c) (* d d)))

simplify77.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05672505
132822242
250012117

prune413.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 23.0b

regimes135.0ms

Accuracy

0% (2.8b remaining)

Error of 26.0b against oracle of 23.2b and baseline of 26.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample898.0ms

Algorithm
intervals
Results
674.0ms8488×body80valid