Details

Time bar (total: 4.2s)

sample20.0ms

Algorithm
intervals
Results
10.0ms268×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(- (* b c) (* a d))
27.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite21.0ms

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:
7.0ms
(+ (* c c) (* d d))
4.0ms
(- (* b c) (* a d))
9.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series148.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
39.0ms
(- (* b c) (* a d))
82.0ms
(/ (- (* 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

prune193.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b
(- (* b c) (* a d))
18.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite33.0ms

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:
5.0ms
(/ 1 (* (hypot c d) 1))
14.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series383.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (* (hypot c d) 1))
176.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
37.0ms
(- (* b c) (* a d))
117.0ms
(/ (- (* 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

prune323.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.3b
(- (* b c) (* a d))
18.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
1.0ms
(hypot c d)
8.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series316.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot c d)
115.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04581435
116671331
250011322

prune364.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
0.3b
(- (* b c) (* a d))
0.4b
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
18.2b
(/ (hypot c d) (- (* b c) (* a d)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
255×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
39×associate-/r/
36×add-exp-log
23×div-inv
22×div-exp
21×associate-/r*
20×add-cbrt-cube
18×flip3-- flip--
10×cbrt-undiv
6×add-log-exp
5×pow1
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
3×frac-2neg clear-num
1×sub-neg pow-flip fma-neg diff-log prod-diff associate-/l/ inv-pow
Counts
4 → 359
Calls
4 calls:
17.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
4.0ms
(- (* b c) (* a d))
8.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
5.0ms
(/ (hypot c d) (- (* b c) (* a d)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
37.0ms
(- (* b c) (* a d))
107.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
85.0ms
(/ (hypot c d) (- (* b c) (* a d)))

simplify74.0ms

Algorithm
egg-herbie
Counts
371 → 371
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012945404
150014894

prune782.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes180.0ms

Accuracy

22.7% (9.2b remaining)

Error of 14.0b against oracle of 4.7b and baseline of 16.7b

bsearch116.0ms

Steps
ItersRangePoint
8
6.736236834044166e+174
2.543242481922855e+177
6.8023434970335964e+174
9
-5.99961992380576e-270
-2.2239357130567353e-275
-1.0119004740350262e-272
8
-4.617021828322126e+139
-2.519325379392933e+135
-4.286619182115773e+139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03822
13922
23922

end0.0ms

sample518.0ms

Algorithm
intervals
Results
309.0ms8469×body80valid