Details

Time bar (total: 5.5s)

sample26.0ms

Algorithm
intervals
Results
14.0ms275×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
28.7b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
8.0ms
(+ (* c c) (* d d))
8.0ms
(- (* b c) (* a d))
26.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series140.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* c c) (* d d))
37.0ms
(- (* b c) (* a d))
78.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0314555
11341496
25001481

prune348.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
16.9b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
11.0ms
(/ 1 (* (hypot c d) 1))
52.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
9.0ms
(- (* b c) (* a d))
23.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series347.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ 1 (* (hypot c d) 1))
157.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
104.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify61.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05531207
123041003
25001995

prune605.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b
(- (* b c) (* a d))
16.9b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
22.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
8.0ms
(- (* b c) (* a d))
19.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series248.0ms

Counts
3 → 9
Calls
3 calls:
109.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
34.0ms
(- (* b c) (* a d))
106.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04491408
116571307
250011298

prune920.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (hypot c d)))
0.5b
(- (* b c) (* a d))
5.6b
(* (/ 1 (sqrt (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
11.3b
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
94×times-frac
66×*-un-lft-identity
60×add-cube-cbrt
53×sqrt-prod
32×add-exp-log
22×associate-*r* associate-*l*
20×add-cbrt-cube
15×unswap-sqr
12×associate-/r*
11×div-exp
8×pow1 prod-exp
6×cbrt-undiv associate-/l* add-log-exp
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp pow-flip 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 192
Calls
4 calls:
7.0ms
(/ 1 (sqrt (hypot c d)))
9.0ms
(- (* b c) (* a d))
49.0ms
(* (/ 1 (sqrt (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
20.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (sqrt (hypot c d)))
34.0ms
(- (* b c) (* a d))
102.0ms
(* (/ 1 (sqrt (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
176.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

simplify87.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06712149
132151896
250011778

prune1.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes277.0ms

Accuracy

32.6% (8.4b remaining)

Error of 13.2b against oracle of 4.9b and baseline of 17.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03534
13534

end0.0ms

sample634.0ms

Algorithm
intervals
Results
416.0ms8508×body80valid