Details

Time bar (total: 3.9s)

sample23.0ms

Algorithm
intervals
Results
9.0ms276×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: 28.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.7b
(- (* b c) (* a d))
27.5b
(/ (- (* 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:
7.0ms
(+ (* c c) (* d d))
10.0ms
(- (* b c) (* a d))
24.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series137.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* c c) (* d d))
35.0ms
(- (* b c) (* a d))
77.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune188.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.4b

localize11.0ms

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))
16.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite81.0ms

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)
51.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
8.0ms
(- (* b c) (* a d))
18.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series346.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(hypot c d)
163.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
34.0ms
(- (* b c) (* a d))
107.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify62.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05441122
12247931
25003929

prune300.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.7b
(- (* b c) (* a d))
16.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite51.0ms

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)
18.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
10.0ms
(- (* b c) (* a d))
18.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series289.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(hypot c d)
107.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
37.0ms
(- (* b c) (* a d))
105.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify50.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04581435
116671331
250011322

prune389.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (sqrt (hypot c d)) (hypot c d)))
0.7b
(- (* b c) (* a d))
8.6b
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))
17.6b
(* (/ 1 (* (sqrt (hypot c d)) (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
45×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt *-un-lft-identity
32×add-cbrt-cube
23×prod-exp
22×associate-*r* sqrt-prod
20×div-exp
13×pow1
10×cbrt-undiv
9×cbrt-unprod
7×pow-flip associate-*l* associate-/r*
6×rec-exp 1-exp associate-/l* add-log-exp
4×expm1-log1p-u log1p-expm1-u div-inv
3×unswap-sqr
2×flip3-- frac-2neg sqrt-pow1 pow-plus pow1/2 pow-prod-down clear-num pow-prod-up flip-- associate-/l/
1×frac-times sub-neg cube-unmult fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 161
Calls
4 calls:
16.0ms
(/ 1 (* (sqrt (hypot c d)) (hypot c d)))
8.0ms
(- (* b c) (* a d))
19.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))
71.0ms
(* (/ 1 (* (sqrt (hypot c d)) (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ 1 (* (sqrt (hypot c d)) (hypot c d)))
34.0ms
(- (* b c) (* a d))
181.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))
163.0ms
(* (/ 1 (* (sqrt (hypot c d)) (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))

simplify81.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06461820
130701533
250011427

prune370.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

regimes181.0ms

Accuracy

32.2% (8.4b remaining)

Error of 13.2b against oracle of 4.8b and baseline of 17.2b

bsearch104.0ms

Steps
ItersRangePoint
9
1.0826531041751224e+149
1.7435338617608826e+156
1.368280955057291e+154
7
1.1952581674532207e-17
4.3612806898142137e-16
1.0980505939332989e-16
11
-3.555858957855583e+230
-3.907040633350073e+205
-5.457377104622506e+208

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14124
24124

end0.0ms

sample575.0ms

Algorithm
intervals
Results
276.0ms8506×body80valid