Details

Time bar (total: 3.9s)

sample20.0ms

Algorithm
intervals
Results
10.0ms269×body80valid

simplify13.0ms

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: 26.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.7b
(- (* b c) (* a d))
25.6b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

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:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* c c) (* d d))
38.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune193.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.7b
(- (* b c) (* a d))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
32×prod-exp
27×add-cbrt-cube
26×add-sqr-sqrt
23×div-exp
22×times-frac
21×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×pow1 rec-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 120
Calls
4 calls:
0.0ms
(hypot c d)
24.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series376.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot c d)
177.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
40.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify60.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05441122
12247931
25003929

prune313.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

localize13.0ms

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))
0.7b
(- (* b c) (* a d))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite24.0ms

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:
0.0ms
(hypot c d)
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series313.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(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))

simplify53.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04581435
116671331
250011322

prune359.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b
(* (sqrt (/ 1 (* (hypot c d) 1))) (* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d))))
0.7b
(- (* b c) (* a d))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
26×times-frac
25×add-cube-cbrt *-un-lft-identity
20×add-exp-log associate-*l* add-cbrt-cube
16×sqrt-prod
14×associate-*r*
11×pow1
10×sqrt-div
7×prod-exp cbrt-unprod
6×frac-times associate-*r/ add-log-exp
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u div-inv unswap-sqr
3×cbrt-undiv div-exp associate-/r* associate-/l*
2×flip3-- *-commutative flip-- associate-/l/
1×sub-neg frac-2neg fma-neg diff-log div-sub prod-diff clear-num
Counts
4 → 129
Calls
4 calls:
28.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d)))
58.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d))))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series574.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d)))
172.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d))))
40.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify78.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
05251554
126651314
250011267

prune383.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.3b

regimes251.0ms

Accuracy

31.6% (8.7b remaining)

Error of 13.6b against oracle of 4.9b and baseline of 17.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04441
14841
24941
34941

end0.0ms

sample532.0ms

Algorithm
intervals
Results
322.0ms8464×body80valid