Details

Time bar (total: 3.5s)

sample22.0ms

Algorithm
intervals
Results
12.0ms274×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: 26.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(- (* b c) (* a d))
26.0b
(/ (- (* 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)))

series149.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
37.0ms
(- (* b c) (* a d))
83.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0314555
11341496
25001481

prune197.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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))
3.0ms
(- (* b c) (* a d))
23.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series383.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (* (hypot c d) 1))
40.0ms
(- (* b c) (* a d))
174.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05531207
123041003
25001995

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.2b
(- (* b c) (* a d))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

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:
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))

series269.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
40.0ms
(- (* b c) (* a d))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify54.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04491408
116571307
250011298

prune312.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* b c) (hypot c d)) (hypot c d))
1.0b
(/ (/ (* a d) (hypot c d)) (hypot c d))
9.1b
(/ (* a d) (hypot c d))
12.6b
(/ (* b c) (hypot c d))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
16×associate-/l*
14×cbrt-undiv div-exp
12×associate-/r* div-inv
4×pow1 expm1-log1p-u frac-2neg prod-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 146
Calls
4 calls:
5.0ms
(/ (/ (* b c) (hypot c d)) (hypot c d))
8.0ms
(/ (/ (* a d) (hypot c d)) (hypot c d))
3.0ms
(/ (* a d) (hypot c d))
3.0ms
(/ (* b c) (hypot c d))

series272.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (/ (* b c) (hypot c d)) (hypot c d))
69.0ms
(/ (/ (* a d) (hypot c d)) (hypot c d))
68.0ms
(/ (* a d) (hypot c d))
65.0ms
(/ (* b c) (hypot c d))

simplify57.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04951158
121661010
25001996

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

regimes181.0ms

Accuracy

52.8% (4.0b remaining)

Error of 4.8b against oracle of 0.8b and baseline of 9.3b

bsearch74.0ms

Steps
ItersRangePoint
8
4.474924955551132e-38
1.5214700919419666e-35
1.0382708421545201e-35
7
-1.1049075135714818e+81
-5.355145492118649e+78
-2.2616143508082277e+79

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03423
13623
23623

end0.0ms

sample538.0ms

Algorithm
intervals
Results
316.0ms8457×body80valid