Details

Time bar (total: 3.4s)

sample20.0ms

Algorithm
intervals
Results
10.0ms270×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
21.4b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

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)))

series155.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* c c) (* d d))
38.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* 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

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize13.0ms

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)))
0.5b
(- (* b c) (* a d))
12.6b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite45.0ms

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:
4.0ms
(/ 1 (* (hypot c d) 1))
26.0ms
(* (/ 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))

series390.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (* (hypot c d) 1))
180.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
42.0ms
(- (* b c) (* a d))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify67.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05531207
123041003
25001995

prune320.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
0.5b
(- (* b c) (* a d))
12.6b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
5×add-log-exp
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg 1-exp clear-num flip-- cbrt-unprod
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 99
Calls
3 calls:
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series274.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
42.0ms
(- (* b c) (* a d))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify46.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0421962
11690852
25001851

prune278.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.0b
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
0.5b
(- (* b c) (* a d))
12.6b
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×add-cbrt-cube
27×add-sqr-sqrt
26×prod-exp
25×div-exp
21×*-un-lft-identity times-frac
20×add-cube-cbrt
13×associate-*r*
10×cbrt-undiv 1-exp
9×cbrt-unprod
7×pow1
6×associate-/l/ add-log-exp
5×rec-exp flip3-- flip--
4×expm1-log1p-u frac-times associate-*l/ associate-/r* log1p-expm1-u associate-/l*
3×associate-*l* div-inv unswap-sqr
2×frac-2neg associate-*r/ clear-num un-div-inv
1×sub-neg pow-flip fma-neg diff-log prod-diff pow-prod-down *-commutative inv-pow
Counts
4 → 133
Calls
4 calls:
2.0ms
(/ 1 (hypot c d))
12.0ms
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
3.0ms
(- (* b c) (* a d))
14.0ms
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (hypot c d))
122.0ms
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
38.0ms
(- (* b c) (* a d))
116.0ms
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify61.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05221094
12270875
25002842

prune282.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

regimes183.0ms

Accuracy

16% (9.9b remaining)

Error of 14.6b against oracle of 4.8b and baseline of 16.5b

bsearch44.0ms

Steps
ItersRangePoint
9
6.7885585141402705e+103
7.826509235711787e+111
7.198676858313622e+111

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02512
12912
22912

end0.0ms

sample524.0ms

Algorithm
intervals
Results
312.0ms8454×body80valid